Greatest Common Factor of 675 and 678

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 675, 678 i.e. 3 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 675 and 678 is 3.

GCF(675,678) = 3

GCF of 675 and 678

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

GCF of:
and

Greatest Common Factor of 675 and 678

GCF of 675 and 678 is 3

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

Prime Factorization of 678


2 678
3 339
113 113
1

Prime factors of 678 are 2,3,113. Prime factorization of 678 in exponential form is:

678 = 21×31×1131

∴ So by taking common prime factors GCF of 675 and 678 is 3

Greatest Common Factor of 675 and 678 by matching factors method

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

Factors of 678

List of positive integer factors of 678 that divides 678 without a remainder.

1,2,3,6,113,226,339,678

Greatest Common Factor

We found the factors and prime factorization of 675 and 678. The biggest common factor number is the GCF number.
So the greatest common factor 675 and 678 is 3.

Also check out the Least Common Multiple of 675 and 678

Properties of GCF 675 and 678

(i) The GCF of 675 and 678 is associative

GCF of 675 and 678 = GCF of 678 and 675

Related Greatest Common Factor of 675

Related Greatest Common Factor of 678

Frequently Asked Questions on GCF of 675 and 678

1. What is the GCF of 675 and 678?

Answer: GCF of 675 and 678 is 3.

2. 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.

3. What are the Factors of 678?

Answer: Factors of 678 are 1, 2, 3, 6, 113, 226, 339, 678. There are 8 integers that are factors of 678. The greatest factor of 678 is 678.

4. How to Find the GCF of 675 and 678?

Answer:

Greatest Common Factor of 675 and 678 = 3

Step 1: Find the prime factorization of 675

675 = 3 x 3 x 3 x 5 x 5

Step 2: Find the prime factorization of 678

678 = 2 x 3 x 113

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 675 and 678 is 3