Greatest Common Factor of 130 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 130, 138 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 130 and 138 is 2.

GCF(130,138) = 2

GCF of 130 and 138

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

GCF of:
and

Greatest Common Factor of 130 and 138

GCF of 130 and 138 is 2

Prime Factorization of 130


2 130
5 65
13 13
1

Prime factors of 130 are 2,5,13. Prime factorization of 130 in exponential form is:

130 = 21×51×131

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 130 and 138 is 2

Greatest Common Factor of 130 and 138 by matching factors method

Factors of 130

List of positive integer factors of 130 that divides 130 without a remainder.

1,2,5,10,13,26,65,130

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 130 and 138. The biggest common factor number is the GCF number.
So the greatest common factor 130 and 138 is 2.

Also check out the Least Common Multiple of 130 and 138

Properties of GCF 130 and 138

(i) The GCF of 130 and 138 is associative

GCF of 130 and 138 = GCF of 138 and 130

Related Greatest Common Factor of 130

Related Greatest Common Factor of 138

Frequently Asked Questions on GCF of 130 and 138

1. What is the GCF of 130 and 138?

Answer: GCF of 130 and 138 is 2.

2. What are the Factors of 130?

Answer: Factors of 130 are 1, 2, 5, 10, 13, 26, 65, 130. There are 8 integers that are factors of 130. The greatest factor of 130 is 130.

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 130 and 138?

Answer:

Greatest Common Factor of 130 and 138 = 2

Step 1: Find the prime factorization of 130

130 = 2 x 5 x 13

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 = 2

Step 4: Therefore, the greatest common factor of 130 and 138 is 2