GCF of 64 and 72
2026-02-28 15:48 Diff
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Last updated on September 18, 2025

The GCF is the largest number that can divide two or more numbers without leaving any remainder. GCF is used to share the items equally, to group or arrange items, and schedule events. In this topic, we will learn about the GCF of 64 and 72.

What is the GCF of 64 and 72?

The greatest common factor of 64 and 72 is 8. The largest divisor of two or more numbers is called the GCF of the number. If two numbers are co-prime, they have no common factors other than 1, so their GCF is 1.

The GCF of two numbers cannot be negative because divisors are always positive.

How to find the GCF of 64 and 72?

To find the GCF of 64 and 72, a few methods are described below 

  • Listing Factors 
     
  • Prime Factorization
     
  • Long Division Method / by Euclidean Algorithm

GCF of 64 and 72 by Using Listing of Factors

Steps to find the GCF of 64 and 72 using the listing of factors

Step 1: Firstly, list the factors of each number

Factors of 64 = 1, 2, 4, 8, 16, 32, 64.

Factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.

Step 2: Now, identify the common factors of them Common factors of 64 and 72: 1, 2, 4, 8.

Step 3: Choose the largest factor The largest factor that both numbers have is 8. The GCF of 64 and 72 is 8.

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GCF of 64 and 72 Using Prime Factorization

To find the GCF of 64 and 72 using Prime Factorization Method, follow these steps:

Step 1: Find the prime Factors of each number

Prime Factors of 64: 64 = 2 × 2 × 2 × 2 × 2 × 2 = 26

Prime Factors of 72: 72 = 2 × 2 × 2 × 3 × 3 = 23 × 32

Step 2: Now, identify the common prime factors The common prime factors are: 2 × 2 × 2 = 23

Step 3: Multiply the common prime factors 2^3 = 8. The Greatest Common Factor of 64 and 72 is 8.

GCF of 64 and 72 Using Division Method or Euclidean Algorithm Method

Find the GCF of 64 and 72 using the division method or Euclidean Algorithm Method. Follow these steps:

Step 1: First, divide the larger number by the smaller number Here, divide 72 by 64 72 ÷ 64 = 1 (quotient), The remainder is calculated as 72 − (64×1) = 8 The remainder is 8, not zero, so continue the process

Step 2: Now divide the previous divisor (64) by the previous remainder (8) Divide 64 by 8 64 ÷ 8 = 8 (quotient), remainder = 64 − (8×8) = 0 The remainder is zero, the divisor will become the GCF. The GCF of 64 and 72 is 8.

Common Mistakes and How to Avoid Them in GCF of 64 and 72

Finding GCF of 64 and 72 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.

Problem 1

A cook has 64 cups of flour and 72 cups of sugar. She wants to divide them into the largest equal portions possible. How many cups will be in each portion?

Okay, lets begin

We should find GCF of 64 and 72 GCF of 64 and 72 23 = 8.

There are 8 equal portions 64 ÷ 8 = 8 72 ÷ 8 = 9

There will be 8 portions, and each portion gets 8 cups of flour and 9 cups of sugar.

Explanation

As the GCF of 64 and 72 is 8, the cook can make 8 portions.

Now divide 64 and 72 by 8.

Each portion gets 8 cups of flour and 9 cups of sugar.

Well explained 👍

Problem 2

A gardener has 64 tulips and 72 roses. They want to arrange them in rows with the same number of flowers in each row, using the largest possible number of flowers per row. How many flowers will be in each row?

Okay, lets begin

GCF of 64 and 72 23 = 8.

So each row will have 8 flowers.

Explanation

There are 64 tulips and 72 roses.

To find the total number of flowers in each row, we should find the GCF of 64 and 72.

There will be 8 flowers in each row.

Well explained 👍

Problem 3

A contractor has 64 meters of copper wire and 72 meters of aluminum wire. They want to cut both wires into pieces of equal length, using the longest possible length. What should be the length of each piece?

Okay, lets begin

For calculating the longest equal length, we have to calculate the GCF of 64 and 72

The GCF of 64 and 72 23 = 8.

The wire is 8 meters long.

Explanation

For calculating the longest length of the wire, first, we need to calculate the GCF of 64 and 72, which is 8.

The length of each piece of the wire will be 8 meters.

Well explained 👍

Problem 4

A carpenter has two wooden boards, one 64 cm long and the other 72 cm long. He wants to cut them into the longest possible equal pieces, without any wood left over. What should be the length of each piece?

Okay, lets begin

The carpenter needs the longest piece of wood GCF of 64 and 72 23 = 8.

The longest length of each piece is 8 cm.

Explanation

To find the longest length of each piece of the two wooden boards, 64 cm and 72 cm, respectively.

We have to find the GCF of 64 and 72, which is 8 cm.

The longest length of each piece is 8 cm.

Well explained 👍

Problem 5

If the GCF of 64 and ‘b’ is 8, and the LCM is 576. Find ‘b’.

Okay, lets begin

The value of ‘b’ is 72.

Explanation

GCF × LCM = product of the numbers

8 × 576 = 64 × b

4608 = 64b

b = 4608 ÷ 64 = 72

Well explained 👍

FAQs on the Greatest Common Factor of 64 and 72

1.What is the LCM of 64 and 72?

The LCM of 64 and 72 is 576.

2.Is 64 divisible by 2?

Yes, 64 is divisible by 2 because it is an even number.

3.What will be the GCF of any two prime numbers?

The common factor of prime numbers is 1 and the number itself. Since 1 is the only common factor of any two prime numbers, it is said to be the GCF of any two prime numbers.

4.What is the prime factorization of 72?

The prime factorization of 72 is 23 × 32.

5.Are 64 and 72 prime numbers?

No, 64 and 72 are not prime numbers because both of them have more than two factors.

Important Glossaries for GCF of 64 and 72

  • Factors: Factors are numbers that divide the target number completely. For example, the factors of 8 are 1, 2, 4, and 8.
  • Multiple: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 8 are 8, 16, 24, 32, and so on.
  • Prime Factors: These are the factors of a number that are prime numbers and divide the given number completely. For example, the prime factors of 72 are 2 and 3.
  • Remainder: The value left after division when the number cannot be divided evenly. For example, when 9 is divided by 4, the remainder is 1 and the quotient is 2.
  • LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 64 and 72 is 576.

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Hiralee Lalitkumar Makwana

About the Author

Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.

Fun Fact

: She loves to read number jokes and games.