Greatest Common Factor of 672 and 675

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 672, 675 i.e. 3 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 672 and 675 is 3.

GCF(672,675) = 3

GCF of 672 and 675

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

GCF of:
and

Greatest Common Factor of 672 and 675

GCF of 672 and 675 is 3

Prime Factorization of 672


2 672
2 336
2 168
2 84
2 42
3 21
7 7
1

Prime factors of 672 are 2,3,7. Prime factorization of 672 in exponential form is:

672 = 25×31×71

Prime Factorization of 675


3 675
3 225
3 75
5 25
5 5
1

Prime factors of 675 are 3,5. Prime factorization of 675 in exponential form is:

675 = 33×52

∴ So by taking common prime factors GCF of 672 and 675 is 3

Greatest Common Factor of 672 and 675 by matching factors method

Factors of 672

List of positive integer factors of 672 that divides 672 without a remainder.

1,2,3,4,6,7,8,12,14,16,21,24,28,32,42,48,56,84,96,112,168,224,336,672

Factors of 675

List of positive integer factors of 675 that divides 675 without a remainder.

1,3,5,9,15,25,27,45,75,135,225,675

Greatest Common Factor

We found the factors and prime factorization of 672 and 675. The biggest common factor number is the GCF number.
So the greatest common factor 672 and 675 is 3.

Also check out the Least Common Multiple of 672 and 675

Properties of GCF 672 and 675

(i) The GCF of 672 and 675 is associative

GCF of 672 and 675 = GCF of 675 and 672

Related Greatest Common Factor of 672

Related Greatest Common Factor of 675

Frequently Asked Questions on GCF of 672 and 675

1. What is the GCF of 672 and 675?

Answer: GCF of 672 and 675 is 3.

2. What are the Factors of 672?

Answer: Factors of 672 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48, 56, 84, 96, 112, 168, 224, 336, 672. There are 24 integers that are factors of 672. The greatest factor of 672 is 672.

3. What are the Factors of 675?

Answer: Factors of 675 are 1, 3, 5, 9, 15, 25, 27, 45, 75, 135, 225, 675. There are 12 integers that are factors of 675. The greatest factor of 675 is 675.

4. How to Find the GCF of 672 and 675?

Answer:

Greatest Common Factor of 672 and 675 = 3

Step 1: Find the prime factorization of 672

672 = 2 x 2 x 2 x 2 x 2 x 3 x 7

Step 2: Find the prime factorization of 675

675 = 3 x 3 x 3 x 5 x 5

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 672 and 675 is 3