Greatest Common Factor of 560 and 567

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 560, 567 i.e. 7 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 560 and 567 is 7.

GCF(560,567) = 7

GCF of 560 and 567

Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;

GCF of:
and

Greatest Common Factor of 560 and 567

GCF of 560 and 567 is 7

Prime Factorization of 560


2 560
2 280
2 140
2 70
5 35
7 7
1

Prime factors of 560 are 2,5,7. Prime factorization of 560 in exponential form is:

560 = 24×51×71

Prime Factorization of 567


3 567
3 189
3 63
3 21
7 7
1

Prime factors of 567 are 3,7. Prime factorization of 567 in exponential form is:

567 = 34×71

∴ So by taking common prime factors GCF of 560 and 567 is 7

Greatest Common Factor of 560 and 567 by matching factors method

Factors of 560

List of positive integer factors of 560 that divides 560 without a remainder.

1,2,4,5,7,8,10,14,16,20,28,35,40,56,70,80,112,140,280,560

Factors of 567

List of positive integer factors of 567 that divides 567 without a remainder.

1,3,7,9,21,27,63,81,189,567

Greatest Common Factor

We found the factors and prime factorization of 560 and 567. The biggest common factor number is the GCF number.
So the greatest common factor 560 and 567 is 7.

Also check out the Least Common Multiple of 560 and 567

Properties of GCF 560 and 567

(i) The GCF of 560 and 567 is associative

GCF of 560 and 567 = GCF of 567 and 560

Related Greatest Common Factor of 560

Related Greatest Common Factor of 567

Frequently Asked Questions on GCF of 560 and 567

1. What is the GCF of 560 and 567?

Answer: GCF of 560 and 567 is 7.

2. What are the Factors of 560?

Answer: Factors of 560 are 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 35, 40, 56, 70, 80, 112, 140, 280, 560. There are 20 integers that are factors of 560. The greatest factor of 560 is 560.

3. What are the Factors of 567?

Answer: Factors of 567 are 1, 3, 7, 9, 21, 27, 63, 81, 189, 567. There are 10 integers that are factors of 567. The greatest factor of 567 is 567.

4. How to Find the GCF of 560 and 567?

Answer:

Greatest Common Factor of 560 and 567 = 7

Step 1: Find the prime factorization of 560

560 = 2 x 2 x 2 x 2 x 5 x 7

Step 2: Find the prime factorization of 567

567 = 3 x 3 x 3 x 3 x 7

Step 3: Multiply those factors both numbers have in common in steps i) or ii) above to find the gcf:

GCF = 7

Step 4: Therefore, the greatest common factor of 560 and 567 is 7