How to find the greatest common factor - SAT Math
Card 0 of 128
Suppose that 
is an integer such that 
is ten greater than 
. What is the value of 
?
Suppose that
We are given information that m/4 is 10 greater than m/3. We set up an equation where m/4 = m/3 + 10.
We must then give the m variables a common denominator in order to solve for m. Since 3 * 4 = 12, we can use 12 as our denominator for both m variables.
m/4 = m/3 + 10 (Multiply m/4 by 3 in the numerator and denominator.)
3m/12 = m/3 + 10 (Multiply m/3 by 4 in the numerator and denominator.)
3m/12 = 4m/12 + 10 (Subtract 4m/12 on both sides.)
-m/12 = 10 (Multiply both sides by -12.)
m = -120
-120/4 = -30 and -120/3 = -40. -30 is 10 greater than -40.
We are given information that m/4 is 10 greater than m/3. We set up an equation where m/4 = m/3 + 10.
We must then give the m variables a common denominator in order to solve for m. Since 3 * 4 = 12, we can use 12 as our denominator for both m variables.
m/4 = m/3 + 10 (Multiply m/4 by 3 in the numerator and denominator.)
3m/12 = m/3 + 10 (Multiply m/3 by 4 in the numerator and denominator.)
3m/12 = 4m/12 + 10 (Subtract 4m/12 on both sides.)
-m/12 = 10 (Multiply both sides by -12.)
m = -120
-120/4 = -30 and -120/3 = -40. -30 is 10 greater than -40.
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If 
is divisible by 2, 3 and 15, which of the following is also divisible by these numbers?
If
Since v is divisible by 2, 3 and 15, v must be a multiple of 30. Any number that is divisible by both 2 and 15 must be divisible by their product, 30, since this is the least common multiple.
Out of all the answer choices, v + 30 is the only one that equals a multiple of 30.
Since v is divisible by 2, 3 and 15, v must be a multiple of 30. Any number that is divisible by both 2 and 15 must be divisible by their product, 30, since this is the least common multiple.
Out of all the answer choices, v + 30 is the only one that equals a multiple of 30.
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, 
, and 
are positive two-digit integers.
The greatest common divisor of 
and 
is 10.
The greatest common divisor of 
and 
is 9.
The greatest common divisor of 
and 
is 8.
If 
is an integer, which of the following could it be equal to?
The greatest common divisor of
The greatest common divisor of
The greatest common divisor of
If
The greatest common divisor of 
and 
is 10. This means that the prime factorizations of 
and 
must both contain a 2 and a 5.
The greatest common divisor of 
and 
is 9. This means that the prime factorizations of 
and 
must both contain two 3's.
The greatest common divisor of 
and 
is 8. This means that the prime factorizations of 
and 
must both contain three 2's.
Thus:
We substitute these equalities into the given expression and simplify.
Since 
and 
are two-digit integers (equal to 
and 
respectively), we must have 
and 
. Any other factor values for 
or 
will produce three-digit integers (or greater).
is equal to 
, so 
could be either 1 or 2.
Therefore:
or
The greatest common divisor of
The greatest common divisor of
The greatest common divisor of
Thus:
We substitute these equalities into the given expression and simplify.
Since
Therefore:
or
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What's the greatest common factor of 6 and 8?
What's the greatest common factor of 6 and 8?
Greatest common factor is a common factor shared by two or more numbers. Both numbers are even, so let's divide both numbers by two. We get 
. These are prime numbers (factors of one and itsef) in which we are done. Anytime we have two prime numbers or one prime and one composite number, we are finished. So the greatest common factor is 
.
Greatest common factor is a common factor shared by two or more numbers. Both numbers are even, so let's divide both numbers by two. We get
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What's the greatest common factor of 4 and 8?
What's the greatest common factor of 4 and 8?
Greatest common factor is a common factor shared by two or more numbers. 
is a multiple of 
, so let's divide 
for both numbers. We get 
. We are finished as these are the basic numbers. So the greatest common factor is 
.
Greatest common factor is a common factor shared by two or more numbers.
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What's the greatest common factor of 19 and 27?
What's the greatest common factor of 19 and 27?
Greatest common factor is a common factor shared by two or more numbers. 
is a prime number. 
is a composite number. Since we have a prime and composite number, the greatest common factor is 
.
Greatest common factor is a common factor shared by two or more numbers.
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What's the greatest common factor of 24 and 74?
What's the greatest common factor of 24 and 74?
Greatest common factor is a common factor shared by two or more numbers. Both numbers are even, so let's divide two for both numbers. We get 
. We have one prime and one composite number, so we are finished. The greatest common factor is 
.
Greatest common factor is a common factor shared by two or more numbers. Both numbers are even, so let's divide two for both numbers. We get
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What's the greatest common factor of 18 and 243?
What's the greatest common factor of 18 and 243?
Greatest common factor is a common factor shared by two or more numbers. If you know the divisibility rule of 
(sum of digits are divisible by 
), then the answer is just 
as the quotient is 
. We have a prime and composite number. However, if you don't and only know the divisibility rule of 
, then we can divide both numbers by 
to get 
. We do it once more to get 
. Since we divided twice by 
, we multiply these factors and this is our greatest common factor of 
. Our answer is 
.
Greatest common factor is a common factor shared by two or more numbers. If you know the divisibility rule of
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What's the greatest common factor of 33 and 121?
What's the greatest common factor of 33 and 121?
Greatest common factor is a common factor shared by two or more numbers. If you know divisibility rule of 
, then this is the answer. However, this isn't easy to spot, so we will do process of elimination. The numbers are odd and if we have even factors, we never generate odd numbers so 
is wrong. Next, check divisibility rule of 
. The digits of 
add to 
which isn't divisible by 
so 
is wrong. Next, let's divide 
into 
. We get a decimal value and that's wrong since if we consider 
to be a multiple of 
, it should be a whole number and not a decimal. Finally, by dividing 
and 
, it's also 
. This is our answer. To find out if 
is divisible by 
, just add the outside digits and match the middle one. Since it does, 
is divisible by 
.
Greatest common factor is a common factor shared by two or more numbers. If you know divisibility rule of
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What's the greatest common factor of 55 and 80?
What's the greatest common factor of 55 and 80?
These two numbers are definitely divisible by 
. When we divide both numbers by 
, we get 
and 
remaining. Since we have a combination of a prime and composite number, then we can't find any more factors. Our answer is 
.
These two numbers are definitely divisible by
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What's the greatest common factor of 81 and 27?
What's the greatest common factor of 81 and 27?
Let's do some divisibility rules. For 
, the sum of the digits must be divisible by 
.
We have:
They are both good so when we divide both numbers by 
, we get 
. Lastly they are both divisible by 
. So we multiply both factors to get an answer of 
.
Let's do some divisibility rules. For
We have:
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What's the greatest common factor of 2, 6, 9, and 10?
What's the greatest common factor of 2, 6, 9, and 10?
Greatest common factor involves all the numbers in the set. Even though three of the numbers are divisble by 
, 
isn't. The only factor that satisfies all the numbers is 
.
Greatest common factor involves all the numbers in the set. Even though three of the numbers are divisble by
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What's the greatest common factor of 4, 8, 16, and 26?
What's the greatest common factor of 4, 8, 16, and 26?
Although the first three numbers are divisible by 
, 
doesn't divide evenly into 
. The next best factor is 
. The remainder will be 
. This won't go any further as most of the numbers are even except 
. Our final answer is just 
.
Although the first three numbers are divisible by
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What's the greatest common factor of 15, 90, 105, and 225?
What's the greatest common factor of 15, 90, 105, and 225?
We know all of the numbers are divisible by 
so when we divide all the numbers by 
, we have 
. Next, we can divide al of them by 
, because the sum of the digits of all numbers are divisible by 
. So we get 
. This is as best as we can go so now we multiply the factors to get 
as an answer.
We know all of the numbers are divisible by
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What's the greatest common factor of 36, 84, 96, 120, and 264?
What's the greatest common factor of 36, 84, 96, 120, and 264?
Because they are all even and divisible by 
, we can divide each number 
to get 
. Next, let's divide by 
to get 
. We are finished as we have a mixture of prime and composite numbers. We multiply the factors to get 
.
Because they are all even and divisible by
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Find the greatest common factor of 
and 
.
Find the greatest common factor of
The key here is to find the prime factorizations of both numbers and multiplying the common prime factors together:
Both prime factorizations have 
in common, so 
is our answer.
The key here is to find the prime factorizations of both numbers and multiplying the common prime factors together:
Both prime factorizations have
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Suppose that is an integer such that is ten greater than . What is the value of ?
Suppose that
We are given information that m/4 is 10 greater than m/3. We set up an equation where m/4 = m/3 + 10.
We must then give the m variables a common denominator in order to solve for m. Since 3 * 4 = 12, we can use 12 as our denominator for both m variables.
m/4 = m/3 + 10 (Multiply m/4 by 3 in the numerator and denominator.)
3m/12 = m/3 + 10 (Multiply m/3 by 4 in the numerator and denominator.)
3m/12 = 4m/12 + 10 (Subtract 4m/12 on both sides.)
-m/12 = 10 (Multiply both sides by -12.)
m = -120
-120/4 = -30 and -120/3 = -40. -30 is 10 greater than -40.
We are given information that m/4 is 10 greater than m/3. We set up an equation where m/4 = m/3 + 10.
We must then give the m variables a common denominator in order to solve for m. Since 3 * 4 = 12, we can use 12 as our denominator for both m variables.
m/4 = m/3 + 10 (Multiply m/4 by 3 in the numerator and denominator.)
3m/12 = m/3 + 10 (Multiply m/3 by 4 in the numerator and denominator.)
3m/12 = 4m/12 + 10 (Subtract 4m/12 on both sides.)
-m/12 = 10 (Multiply both sides by -12.)
m = -120
-120/4 = -30 and -120/3 = -40. -30 is 10 greater than -40.
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If is divisible by 2, 3 and 15, which of the following is also divisible by these numbers?
If
Since v is divisible by 2, 3 and 15, v must be a multiple of 30. Any number that is divisible by both 2 and 15 must be divisible by their product, 30, since this is the least common multiple.
Out of all the answer choices, v + 30 is the only one that equals a multiple of 30.
Since v is divisible by 2, 3 and 15, v must be a multiple of 30. Any number that is divisible by both 2 and 15 must be divisible by their product, 30, since this is the least common multiple.
Out of all the answer choices, v + 30 is the only one that equals a multiple of 30.
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, , and are positive two-digit integers.
The greatest common divisor of and is 10.
The greatest common divisor of and is 9.
The greatest common divisor of and is 8.
If is an integer, which of the following could it be equal to?
The greatest common divisor of
The greatest common divisor of
The greatest common divisor of
If
The greatest common divisor of and is 10. This means that the prime factorizations of and must both contain a 2 and a 5.
The greatest common divisor of and is 9. This means that the prime factorizations of and must both contain two 3's.
The greatest common divisor of and is 8. This means that the prime factorizations of and must both contain three 2's.
Thus:
We substitute these equalities into the given expression and simplify.
Since and are two-digit integers (equal to and respectively), we must have and . Any other factor values for or will produce three-digit integers (or greater).
is equal to , so could be either 1 or 2.
Therefore:
or
The greatest common divisor of
The greatest common divisor of
The greatest common divisor of
Thus:
We substitute these equalities into the given expression and simplify.
Since
Therefore:
or
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What's the greatest common factor of 6 and 8?
What's the greatest common factor of 6 and 8?
Greatest common factor is a common factor shared by two or more numbers. Both numbers are even, so let's divide both numbers by two. We get . These are prime numbers (factors of one and itsef) in which we are done. Anytime we have two prime numbers or one prime and one composite number, we are finished. So the greatest common factor is .
Greatest common factor is a common factor shared by two or more numbers. Both numbers are even, so let's divide both numbers by two. We get
Compare your answer with the correct one above