Greatest Common Factor of 560 and 564

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, 564 i.e. 4 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 560 and 564 is 4.

GCF(560,564) = 4

GCF of 560 and 564

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

GCF of:
and

Greatest Common Factor of 560 and 564

GCF of 560 and 564 is 4

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 564


2 564
2 282
3 141
47 47
1

Prime factors of 564 are 2,3,47. Prime factorization of 564 in exponential form is:

564 = 22×31×471

∴ So by taking common prime factors GCF of 560 and 564 is 4

Greatest Common Factor of 560 and 564 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 564

List of positive integer factors of 564 that divides 564 without a remainder.

1,2,3,4,6,12,47,94,141,188,282,564

Greatest Common Factor

We found the factors and prime factorization of 560 and 564. The biggest common factor number is the GCF number.
So the greatest common factor 560 and 564 is 4.

Also check out the Least Common Multiple of 560 and 564

Properties of GCF 560 and 564

(i) The GCF of 560 and 564 is associative

GCF of 560 and 564 = GCF of 564 and 560

Related Greatest Common Factor of 560

Related Greatest Common Factor of 564

Frequently Asked Questions on GCF of 560 and 564

1. What is the GCF of 560 and 564?

Answer: GCF of 560 and 564 is 4.

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 564?

Answer: Factors of 564 are 1, 2, 3, 4, 6, 12, 47, 94, 141, 188, 282, 564. There are 12 integers that are factors of 564. The greatest factor of 564 is 564.

4. How to Find the GCF of 560 and 564?

Answer:

Greatest Common Factor of 560 and 564 = 4

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 564

564 = 2 x 2 x 3 x 47

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

GCF = 2 x 2 = 4

Step 4: Therefore, the greatest common factor of 560 and 564 is 4