Greatest Common Factor of 648 and 654

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 648, 654 i.e. 6 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 648 and 654 is 6.

GCF(648,654) = 6

GCF of 648 and 654

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

GCF of:
and

Greatest Common Factor of 648 and 654

GCF of 648 and 654 is 6

Prime Factorization of 648


2 648
2 324
2 162
3 81
3 27
3 9
3 3
1

Prime factors of 648 are 2,3. Prime factorization of 648 in exponential form is:

648 = 23×34

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

∴ So by taking common prime factors GCF of 648 and 654 is 6

Greatest Common Factor of 648 and 654 by matching factors method

Factors of 648

List of positive integer factors of 648 that divides 648 without a remainder.

1,2,3,4,6,8,9,12,18,24,27,36,54,72,81,108,162,216,324,648

Factors of 654

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

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

Greatest Common Factor

We found the factors and prime factorization of 648 and 654. The biggest common factor number is the GCF number.
So the greatest common factor 648 and 654 is 6.

Also check out the Least Common Multiple of 648 and 654

Properties of GCF 648 and 654

(i) The GCF of 648 and 654 is associative

GCF of 648 and 654 = GCF of 654 and 648

Related Greatest Common Factor of 648

Related Greatest Common Factor of 654

Frequently Asked Questions on GCF of 648 and 654

1. What is the GCF of 648 and 654?

Answer: GCF of 648 and 654 is 6.

2. What are the Factors of 648?

Answer: Factors of 648 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 324, 648. There are 20 integers that are factors of 648. The greatest factor of 648 is 648.

3. 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.

4. How to Find the GCF of 648 and 654?

Answer:

Greatest Common Factor of 648 and 654 = 6

Step 1: Find the prime factorization of 648

648 = 2 x 2 x 2 x 3 x 3 x 3 x 3

Step 2: Find the prime factorization of 654

654 = 2 x 3 x 109

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

GCF = 2 x 3 = 6

Step 4: Therefore, the greatest common factor of 648 and 654 is 6