Greatest Common Factor of 567 and 574

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 567, 574 i.e. 7 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 567 and 574 is 7.

GCF(567,574) = 7

GCF of 567 and 574

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

GCF of:
and

Greatest Common Factor of 567 and 574

GCF of 567 and 574 is 7

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

Prime Factorization of 574


2 574
7 287
41 41
1

Prime factors of 574 are 2,7,41. Prime factorization of 574 in exponential form is:

574 = 21×71×411

∴ So by taking common prime factors GCF of 567 and 574 is 7

Greatest Common Factor of 567 and 574 by matching factors method

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

Factors of 574

List of positive integer factors of 574 that divides 574 without a remainder.

1,2,7,14,41,82,287,574

Greatest Common Factor

We found the factors and prime factorization of 567 and 574. The biggest common factor number is the GCF number.
So the greatest common factor 567 and 574 is 7.

Also check out the Least Common Multiple of 567 and 574

Properties of GCF 567 and 574

(i) The GCF of 567 and 574 is associative

GCF of 567 and 574 = GCF of 574 and 567

Related Greatest Common Factor of 567

Related Greatest Common Factor of 574

Frequently Asked Questions on GCF of 567 and 574

1. What is the GCF of 567 and 574?

Answer: GCF of 567 and 574 is 7.

2. 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.

3. What are the Factors of 574?

Answer: Factors of 574 are 1, 2, 7, 14, 41, 82, 287, 574. There are 8 integers that are factors of 574. The greatest factor of 574 is 574.

4. How to Find the GCF of 567 and 574?

Answer:

Greatest Common Factor of 567 and 574 = 7

Step 1: Find the prime factorization of 567

567 = 3 x 3 x 3 x 3 x 7

Step 2: Find the prime factorization of 574

574 = 2 x 7 x 41

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 567 and 574 is 7