Greatest Common Factor of 561 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 561, 564 i.e. 3 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 561 and 564 is 3.

GCF(561,564) = 3

GCF of 561 and 564

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

GCF of:
and

Greatest Common Factor of 561 and 564

GCF of 561 and 564 is 3

Prime Factorization of 561


3 561
11 187
17 17
1

Prime factors of 561 are 3,11,17. Prime factorization of 561 in exponential form is:

561 = 31×111×171

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 561 and 564 is 3

Greatest Common Factor of 561 and 564 by matching factors method

Factors of 561

List of positive integer factors of 561 that divides 561 without a remainder.

1,3,11,17,33,51,187,561

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 561 and 564. The biggest common factor number is the GCF number.
So the greatest common factor 561 and 564 is 3.

Also check out the Least Common Multiple of 561 and 564

Properties of GCF 561 and 564

(i) The GCF of 561 and 564 is associative

GCF of 561 and 564 = GCF of 564 and 561

Related Greatest Common Factor of 561

Related Greatest Common Factor of 564

Frequently Asked Questions on GCF of 561 and 564

1. What is the GCF of 561 and 564?

Answer: GCF of 561 and 564 is 3.

2. What are the Factors of 561?

Answer: Factors of 561 are 1, 3, 11, 17, 33, 51, 187, 561. There are 8 integers that are factors of 561. The greatest factor of 561 is 561.

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 561 and 564?

Answer:

Greatest Common Factor of 561 and 564 = 3

Step 1: Find the prime factorization of 561

561 = 3 x 11 x 17

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 = 3

Step 4: Therefore, the greatest common factor of 561 and 564 is 3