Greatest Common Factor of 135 and 138

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 135, 138 i.e. 3 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 135 and 138 is 3.

GCF(135,138) = 3

GCF of 135 and 138

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

GCF of:
and

Greatest Common Factor of 135 and 138

GCF of 135 and 138 is 3

Prime Factorization of 135


3 135
3 45
3 15
5 5
1

Prime factors of 135 are 3,5. Prime factorization of 135 in exponential form is:

135 = 33×51

Prime Factorization of 138


2 138
3 69
23 23
1

Prime factors of 138 are 2,3,23. Prime factorization of 138 in exponential form is:

138 = 21×31×231

∴ So by taking common prime factors GCF of 135 and 138 is 3

Greatest Common Factor of 135 and 138 by matching factors method

Factors of 135

List of positive integer factors of 135 that divides 135 without a remainder.

1,3,5,9,15,27,45,135

Factors of 138

List of positive integer factors of 138 that divides 138 without a remainder.

1,2,3,6,23,46,69,138

Greatest Common Factor

We found the factors and prime factorization of 135 and 138. The biggest common factor number is the GCF number.
So the greatest common factor 135 and 138 is 3.

Also check out the Least Common Multiple of 135 and 138

Properties of GCF 135 and 138

(i) The GCF of 135 and 138 is associative

GCF of 135 and 138 = GCF of 138 and 135

Related Greatest Common Factor of 135

Related Greatest Common Factor of 138

Frequently Asked Questions on GCF of 135 and 138

1. What is the GCF of 135 and 138?

Answer: GCF of 135 and 138 is 3.

2. What are the Factors of 135?

Answer: Factors of 135 are 1, 3, 5, 9, 15, 27, 45, 135. There are 8 integers that are factors of 135. The greatest factor of 135 is 135.

3. What are the Factors of 138?

Answer: Factors of 138 are 1, 2, 3, 6, 23, 46, 69, 138. There are 8 integers that are factors of 138. The greatest factor of 138 is 138.

4. How to Find the GCF of 135 and 138?

Answer:

Greatest Common Factor of 135 and 138 = 3

Step 1: Find the prime factorization of 135

135 = 3 x 3 x 3 x 5

Step 2: Find the prime factorization of 138

138 = 2 x 3 x 23

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 135 and 138 is 3