Greatest Common Factor of 654 and 656

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 654, 656 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 654 and 656 is 2.

GCF(654,656) = 2

GCF of 654 and 656

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

GCF of:
and

Greatest Common Factor of 654 and 656

GCF of 654 and 656 is 2

Prime Factorization of 654


2 654
3 327
109 109
1

Prime factors of 654 are 2,3,109. Prime factorization of 654 in exponential form is:

654 = 21×31×1091

Prime Factorization of 656


2 656
2 328
2 164
2 82
41 41
1

Prime factors of 656 are 2,41. Prime factorization of 656 in exponential form is:

656 = 24×411

∴ So by taking common prime factors GCF of 654 and 656 is 2

Greatest Common Factor of 654 and 656 by matching factors method

Factors of 654

List of positive integer factors of 654 that divides 654 without a remainder.

1,2,3,6,109,218,327,654

Factors of 656

List of positive integer factors of 656 that divides 656 without a remainder.

1,2,4,8,16,41,82,164,328,656

Greatest Common Factor

We found the factors and prime factorization of 654 and 656. The biggest common factor number is the GCF number.
So the greatest common factor 654 and 656 is 2.

Also check out the Least Common Multiple of 654 and 656

Properties of GCF 654 and 656

(i) The GCF of 654 and 656 is associative

GCF of 654 and 656 = GCF of 656 and 654

Related Greatest Common Factor of 654

Related Greatest Common Factor of 656

Frequently Asked Questions on GCF of 654 and 656

1. What is the GCF of 654 and 656?

Answer: GCF of 654 and 656 is 2.

2. What are the Factors of 654?

Answer: Factors of 654 are 1, 2, 3, 6, 109, 218, 327, 654. There are 8 integers that are factors of 654. The greatest factor of 654 is 654.

3. What are the Factors of 656?

Answer: Factors of 656 are 1, 2, 4, 8, 16, 41, 82, 164, 328, 656. There are 10 integers that are factors of 656. The greatest factor of 656 is 656.

4. How to Find the GCF of 654 and 656?

Answer:

Greatest Common Factor of 654 and 656 = 2

Step 1: Find the prime factorization of 654

654 = 2 x 3 x 109

Step 2: Find the prime factorization of 656

656 = 2 x 2 x 2 x 2 x 41

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

GCF = 2

Step 4: Therefore, the greatest common factor of 654 and 656 is 2