Greatest Common Factor of 654 and 657

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, 657 i.e. 3 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 654 and 657 is 3.

GCF(654,657) = 3

GCF of 654 and 657

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

GCF of:
and

Greatest Common Factor of 654 and 657

GCF of 654 and 657 is 3

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 657


3 657
3 219
73 73
1

Prime factors of 657 are 3,73. Prime factorization of 657 in exponential form is:

657 = 32×731

∴ So by taking common prime factors GCF of 654 and 657 is 3

Greatest Common Factor of 654 and 657 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 657

List of positive integer factors of 657 that divides 657 without a remainder.

1,3,9,73,219,657

Greatest Common Factor

We found the factors and prime factorization of 654 and 657. The biggest common factor number is the GCF number.
So the greatest common factor 654 and 657 is 3.

Also check out the Least Common Multiple of 654 and 657

Properties of GCF 654 and 657

(i) The GCF of 654 and 657 is associative

GCF of 654 and 657 = GCF of 657 and 654

Related Greatest Common Factor of 654

Related Greatest Common Factor of 657

Frequently Asked Questions on GCF of 654 and 657

1. What is the GCF of 654 and 657?

Answer: GCF of 654 and 657 is 3.

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 657?

Answer: Factors of 657 are 1, 3, 9, 73, 219, 657. There are 6 integers that are factors of 657. The greatest factor of 657 is 657.

4. How to Find the GCF of 654 and 657?

Answer:

Greatest Common Factor of 654 and 657 = 3

Step 1: Find the prime factorization of 654

654 = 2 x 3 x 109

Step 2: Find the prime factorization of 657

657 = 3 x 3 x 73

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 654 and 657 is 3