How to find the greatest common factor - ISEE Upper Level (grades 9-12) Quantitative Reasoning
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3/5 + 4/7 – 1/3 =
3/5 + 4/7 – 1/3 =
We need to find a common denominator to add and subtract these fractions. Let's do the addition first. The lowest common denominator of 5 and 7 is 5 * 7 = 35, so 3/5 + 4/7 = 21/35 + 20/35 = 41/35.
Now to the subtraction. The lowest common denominator of 35 and 3 is 35 * 3 = 105, so altogether, 3/5 + 4/7 – 1/3 = 41/35 – 1/3 = 123/105 – 35/105 = 88/105. This does not simplify and is therefore the correct answer.
We need to find a common denominator to add and subtract these fractions. Let's do the addition first. The lowest common denominator of 5 and 7 is 5 * 7 = 35, so 3/5 + 4/7 = 21/35 + 20/35 = 41/35.
Now to the subtraction. The lowest common denominator of 35 and 3 is 35 * 3 = 105, so altogether, 3/5 + 4/7 – 1/3 = 41/35 – 1/3 = 123/105 – 35/105 = 88/105. This does not simplify and is therefore the correct answer.
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25 is the greatest common factor of 175 and which of these numbers?
25 is the greatest common factor of 175 and which of these numbers?
Of the four numbers given, 25 is only a factor of 150, since all multiples of 25 end in the digits 25, 50, 75, or 00. To determine whether 150 is correct, we inspect the factors of 150 and 175:
Factors of 150: 
Factors of 175: 
Since 25 is the greatest number in both lists, 
.
Of the four numbers given, 25 is only a factor of 150, since all multiples of 25 end in the digits 25, 50, 75, or 00. To determine whether 150 is correct, we inspect the factors of 150 and 175:
Factors of 150:
Factors of 175:
Since 25 is the greatest number in both lists,
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is an odd prime.
Which is the greater quantity?
(a) 
(b) 
Which is the greater quantity?
(a)
(b)
The greatest common factor of two numbers is the product of the prime factors they share; if they share no prime factors, it is 
.
(a) 
. Since 
is an odd prime, 
and 
share no prime factors, and 
.
(b) 
, since 
is prime. Since 
is an even prime, 
and 
share no prime factors, and 
.
The quantities are equal since each is equal to 
.
The greatest common factor of two numbers is the product of the prime factors they share; if they share no prime factors, it is
(a)
(b)
The quantities are equal since each is equal to
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Column A Column B
The GCF of The GCF of
45 and 120 38 and 114
Column A Column B
The GCF of The GCF of
45 and 120 38 and 114
There are a couple different ways to find the GCF of a set of numbers. Sometimes it's easiest to make a factor tree for each number. The factors that the pair of numbers have in common are then multiplied to get the GCF. So for 45, the prime factorization ends up being: 
. The prime factorization of 120 is: 
. Since they have a 5 and 3 in common, those are multiplied together to get 15 for the GCF. Repeat the same process for 38 and 114. The prime factorization of 38 is 
. The prime factorization of 114 is 
. Therefore, multiply 19 and 2 to get 38 for their GCF. Column B is greater.
There are a couple different ways to find the GCF of a set of numbers. Sometimes it's easiest to make a factor tree for each number. The factors that the pair of numbers have in common are then multiplied to get the GCF. So for 45, the prime factorization ends up being:
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Annette's family has 
jars of applesauce. In a month, they go through 
jars of apple sauce. How many jars of applesauce remain?
Annette's family has
If Annette's family has 
jars of applesauce, and in a month, they go through 
jars of apple sauce, that means 
jars of applesauce will be left.
The first step to determining how much applesauce is left it to convert the fractions into mixed numbers. This gives us:
The next step is to find a common denominator, which would be 15. This gives us:
If Annette's family has
The first step to determining how much applesauce is left it to convert the fractions into mixed numbers. This gives us:
The next step is to find a common denominator, which would be 15. This gives us:
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What is the greatest common factor of 
and 
?
What is the greatest common factor of
To solve for the greatest common factor, it is necessary to get your numbers into prime factor form. For each of your numbers, this is:
Next, for each of your sets of prime factors, you need to choose the exponent for which you have the smallest value; therefore, for your values, you choose:
: 
: 
: 
: None
: None
Taking these together, you get:
To solve for the greatest common factor, it is necessary to get your numbers into prime factor form. For each of your numbers, this is:
Next, for each of your sets of prime factors, you need to choose the exponent for which you have the smallest value; therefore, for your values, you choose:
Taking these together, you get:
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What is the greatest common factor of 
and 
?
What is the greatest common factor of
To solve for the greatest common factor, it is necessary to get your numbers into prime factor form. For each of your numbers, this is:
Next, for each of your sets of prime factors, you need to choose the exponent for which you have the smallest value; therefore, for your values, you choose:
: None
: 
: None
: None
Taking these together, you get: 
To solve for the greatest common factor, it is necessary to get your numbers into prime factor form. For each of your numbers, this is:
Next, for each of your sets of prime factors, you need to choose the exponent for which you have the smallest value; therefore, for your values, you choose:
Taking these together, you get:
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What is the greatest common factor of 
and 
?
What is the greatest common factor of
To solve for the greatest common factor, it is necessary to get your numbers into prime factor form. For each of your numbers, this is:
Next, for each of your sets of prime factors, you need to choose the exponent for which you have the smallest value; therefore, for your values, you choose:
: 
: None
: None
: None
Taking these together, you get: 
To solve for the greatest common factor, it is necessary to get your numbers into prime factor form. For each of your numbers, this is:
Next, for each of your sets of prime factors, you need to choose the exponent for which you have the smallest value; therefore, for your values, you choose:
Taking these together, you get:
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, 
, 
, 
, and 
are five distinct prime integers. Give the greatest common factor of 
and 
.
If two integers are broken down into their prime factorizations, their greatest common factor is the product of their common prime factors.
Since 
, 
, 
, 
, and 
are distinct prime integers, the two expressions can be factored into their prime factorizations as follows - with their common prime factors underlined:
The greatest common factor is the product of those three factors, or 
.
If two integers are broken down into their prime factorizations, their greatest common factor is the product of their common prime factors.
Since
The greatest common factor is the product of those three factors, or
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