Greatest Common Factor

What is a prime number?

• A whole number that can be divided evenly by multiple numbers.

• A whole number greater than 1 that has only two factors: 1 and itself.

• A whole number that is greater than 1 and has more than two factors.

• A whole number that is smaller than 1 and has no factors.

Answer explanation

A prime number is a whole number that is greater than 1 and has exactly two factors: 1 and itself. In other words, it cannot be divided by any other whole number apart from 1 and the number itself without leaving a remainder. For example, 3 is a prime number because it only has two factors: 1 and 3.

Is 2 a prime number?

• Yes, because it only has two factors: 1 and itself.

• No, because it has more than two factors.

• Yes, because it is the smallest positive integer.

• No, because it can be divided by 1, 2, and other numbers without leaving a remainder.

Answer explanation

A prime number is a whole number greater than 1 that has exactly two factors: 1 and itself. The factors of 2 are 1 and 2, and no other whole number divides into 2 without leaving a remainder. Therefore, 2 is a prime number. It is the smallest prime number and serves as the starting point for the set of prime numbers.

What is the greatest common factor (GCF)?

• The smallest number that divides into two or more given numbers with no remainder.

• The average of two or more given numbers.

• The largest number that multiplies two or more given numbers.

• The largest factor two or more numbers have in common. It is the largest number that divides into two or more given numbers without leaving a remainder.

Answer explanation

The greatest common factor (GCF), also known as the highest common factor, is the largest factor two or more numbers have in common. It is the largest number that divides into two or more given numbers without leaving a remainder. It is useful for simplifying fractions and solving everyday problems. 

What is the greatest common factor (GCF) of 12 and 28?

• 2

• 3

• 4

• 7

Answer explanation

To find the GCF of 12 and 28 using prime factorization, you need to determine the common prime factors and multiply them together. Break down both numbers into their prime factors:

12: 2 × 2 × 3

28: 2 × 2 × 7

Now, identify the common prime factors, which are the prime numbers that appear in both factorizations. In this case, the common prime factors are 2 and 2.

Finally, multiply the common prime factors together to find the GCF. In this example, the GCF is 4, since 2 × 2 = 4.

What is the greatest common factor (GCF) of 24 and 60?

• 12

• 3

• 4

• 6

Answer explanation

Explanation: To find the GCF of 24 and 60 using prime factorization, you need to determine the common prime factors and multiply them together. Break down both numbers into their prime factors:

24: 2 × 2 × 2 × 3

60: 2 × 2 × 3 × 5

Now, identify the common prime factors, which are the prime numbers that appear in both factorizations. In this case, the common prime factors are 2, 2, and 3.

Finally, multiply the common prime factors together to find the GCF. In this example, the GCF is 2 × 2 × 3 = 12.

What is the greatest common factor (GCF) of 56 and 84?

• 14  

• 28

• 7

• 21

Answer explanation

To find the GCF of 56 and 84 using prime factorization, you need to determine the common prime factors and multiply them together. Break down both numbers into their prime factors:

Prime factorization of 56: 2 × 2 × 2 × 7  

Prime factorization of 84: 2 × 2 × 3 × 7  

Now, identify the common prime factors, which are the prime numbers that appear in both factorizations. In this case, the common prime factors are 2, 2, and 7.

Finally, multiply the common prime factors together to find the GCF. In this example, the GCF is 2 × 2 × 7 = 28.

What is the greatest common factor (GCF) of 72 and 120?

• 24  

• 48

• 36

• 18

Answer explanation

To find the GCF of 72 and 120 using prime factorization, you need to determine the common prime factors and multiply them together. Break down both numbers into their prime factors:

Prime factorization of 72: 2 × 2 × 2 × 3 × 3  

Prime factorization of 120: 2 × 2 × 2 × 3 × 5  

Now, identify the common prime factors, which are the prime numbers that appear in both factorizations. In this case, the common prime factors are 2, 2, 2, and 3.

Finally, multiply the common prime factors together to find the GCF. In this example, the GCF is 2 × 2 × 2 × 3 = 24.

What is the GCF of 90 and 135?

• 15

• 30 

• 45

• 60

Answer explanation

To find the GCF of 90 and 135 using prime factorization, you need to determine the common prime factors and multiply them together. Break down both numbers into their prime factors:

Prime factorization of 90: 2 × 3 × 3 × 5  

Prime factorization of 135: 3 × 3 × 3 × 5  

Now, identify the common prime factors, which are the prime numbers that appear in both factorizations. In this case, the common prime factors are 3, 3, and 5.

Finally, multiply the common prime factors together to find the GCF. In this example, the GCF is 3 × 3 × 5 = 45.

Calculate the GCF of 66 and 99.

• 44

• 33

• 22

• 11

Answer explanation

To find the GCF of 66 and 99 using prime factorization, you need to determine the common prime factors and multiply them together. Break down both numbers into their prime factors:

Prime factorization of 66: 2 × 3 × 11  

Prime factorization of 99: 3 × 3 × 11  

Now, identify the common prime factors, which are the prime numbers that appear in both factorizations. In this case, the common prime factors are 3 and 11.

Finally, multiply the common prime factors together to find the GCF. In this example, the GCF is 3 × 11 = 33.

Find the GCF of 80 and 120.

• 30

• 20

• 60

• 40

Answer explanation

To find the GCF of 80 and 120 using prime factorization, you need to determine the common prime factors and multiply them together. Break down both numbers into their prime factors:

Prime factorization of 80: 2 × 2 × 2 × 2 × 5  

Prime factorization of 120: 2 × 2 × 2 × 3 × 5  

Now, identify the common prime factors, which are the prime numbers that appear in both factorizations. In this case, the common prime factors are 2, 2, 2, and 5.

Finally, multiply the common prime factors together to find the GCF. In this example, the GCF is 2 × 2 × 2 × 5 = 40.