GCF of 64 and 56
2026-02-21 20:32 Diff
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Last updated on August 13, 2025

The GCF is the largest number that can divide two or more numbers without leaving any remainder. GCF is used to share items equally, to group or arrange items, and schedule events. In this topic, we will learn about the GCF of 64 and 56.

What is the GCF of 64 and 56?

The greatest common factor of 64 and 56 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 56?

To find the GCF of 64 and 56, a few methods are described below -

  1. Listing Factors
  2. Prime Factorization
  3. Long Division Method / by Euclidean Algorithm

GCF of 64 and 56 by Using Listing of factors

Steps to find the GCF of 64 and 56 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 56 = 1, 2, 4, 7, 8, 14, 28, 56.

Step 2: Now, identify the common factors of them Common factors of 64 and 56: 1, 2, 4, 8.

Step 3: Choose the largest factor The largest factor that both numbers have is 8. The GCF of 64 and 56 is 8.

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GCF of 64 and 56 Using Prime Factorization

To find the GCF of 64 and 56 using the Prime Factorization Method, follow these steps:

Step 1: Find the prime factors of each number Prime Factors of 64: 64 = 2 x 2 x 2 x 2 x 2 x 2 = 26

Prime Factors of 56: 56 = 2 x 2 x 2 x 7 = 23 x 7

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

Step 3: Multiply the common prime factors 23 = 8. The Greatest Common Factor of 64 and 56 is 8.

GCF of 64 and 56 Using Division Method or Euclidean Algorithm Method

Find the GCF of 64 and 56 using the division method or Euclidean Algorithm Method. Follow these steps:

Step 1: First, divide the larger number by the smaller number Here, divide 64 by 56 64 ÷ 56 = 1 (quotient), The remainder is calculated as 64 − (56×1) = 8 The remainder is 8, not zero, so continue the process

Step 2: Now divide the previous divisor (56) by the previous remainder (8) Divide 56 by 8 56 ÷ 8 = 7 (quotient), remainder = 56 − (8×7) = 0

The remainder is zero, the divisor will become the GCF. The GCF of 64 and 56 is 8.

Common Mistakes and How to Avoid Them in GCF of 64 and 56

Finding GCF of 64 and 56 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 farmer has 64 apples and 56 oranges. He wants to pack them into boxes with the largest number of fruits in each box. How many fruits will be in each box?

Okay, lets begin

We should find the GCF of 64 and 56 GCF of 64 and 56 23 = 8.

There are 8 equal groups 64 ÷ 8 = 8 56 ÷ 8 = 7

There will be 8 boxes, and each box gets 8 apples and 7 oranges.

Explanation

As the GCF of 64 and 56 is 8, the farmer can make 8 boxes. Now divide 64 and 56 by 8. Each box gets 8 apples and 7 oranges.

Well explained 👍

Problem 2

A school has 64 red chairs and 56 blue chairs. They want to arrange them in rows with the same number of chairs in each row, using the largest possible number of chairs per row. How many chairs will be in each row?

Okay, lets begin

GCF of 64 and 56 23 = 8. So each row will have 8 chairs.

Explanation

There are 64 red and 56 blue chairs. To find the total number of chairs in each row, we should find the GCF of 64 and 56. There will be 8 chairs in each row.

Well explained 👍

Problem 3

A tailor has 64 meters of red ribbon and 56 meters of blue ribbon. She wants to cut both ribbons into pieces of equal length, using the longest possible length. What should be the length of each piece?

Okay, lets begin

For calculating longest equal length, we have to calculate the GCF of 64 and 56 The GCF of 64 and 56 23 = 8. The ribbon is 8 meters long.

Explanation

For calculating the longest length of the ribbon first we need to calculate the GCF of 64 and 56 which is 8. The length of each piece of the ribbon will be 8 meters.

Well explained 👍

Problem 4

A carpenter has two wooden planks, one 64 cm long and the other 56 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 56 23 = 8. The longest length of each piece is 8 cm.

Explanation

To find the longest length of each piece from the two wooden planks, 64 cm and 56 cm respectively, we have to find the GCF of 64 and 56, which is 8 cm. The longest length of each piece is 8 cm.

Well explained 👍

Problem 5

If the GCF of 64 and ‘a’ is 8, and the LCM is 448. Find ‘a’.

Okay, lets begin

The value of ‘a’ is 56.

Explanation

GCF x LCM = product of the numbers

8 × 448 = 64 × a

3584 = 64a

a = 3584 ÷ 64 = 56

Well explained 👍

FAQs on the Greatest Common Factor of 64 and 56

1.What is the LCM of 64 and 56?

The LCM of 64 and 56 is 448.

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 56?

The prime factorization of 56 is 23 x 7.

5.Are 64 and 56 prime numbers?

No, 64 and 56 are not prime numbers because both of them have more than two factors.

Important Glossaries for GCF of 64 and 56

  • Factors: Factors are numbers that divide the target number completely. For example, the factors of 16 are 1, 2, 4, 8, and 16.
  • Multiple: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 4 are 4, 8, 12, 16, 20, 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 28 are 2 and 7.
  • Remainder: The value left after division when the number cannot be divided evenly. For example, when 15 is divided by 4, the remainder is 3 and the quotient is 3.
  • GCF: The largest factor that commonly divides two or more numbers. For example, the GCF of 48 and 60 will be 12, as it is their largest common factor that divides the numbers completely.

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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.