Greatest Common Factor of 138 and 140

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 138, 140 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 138 and 140 is 2.

GCF(138,140) = 2

GCF of 138 and 140

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

GCF of:
and

Greatest Common Factor of 138 and 140

GCF of 138 and 140 is 2

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

Prime Factorization of 140


2 140
2 70
5 35
7 7
1

Prime factors of 140 are 2,5,7. Prime factorization of 140 in exponential form is:

140 = 22×51×71

∴ So by taking common prime factors GCF of 138 and 140 is 2

Greatest Common Factor of 138 and 140 by matching factors method

Factors of 138

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

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

Factors of 140

List of positive integer factors of 140 that divides 140 without a remainder.

1,2,4,5,7,10,14,20,28,35,70,140

Greatest Common Factor

We found the factors and prime factorization of 138 and 140. The biggest common factor number is the GCF number.
So the greatest common factor 138 and 140 is 2.

Also check out the Least Common Multiple of 138 and 140

Properties of GCF 138 and 140

(i) The GCF of 138 and 140 is associative

GCF of 138 and 140 = GCF of 140 and 138

Related Greatest Common Factor of 138

Related Greatest Common Factor of 140

Frequently Asked Questions on GCF of 138 and 140

1. What is the GCF of 138 and 140?

Answer: GCF of 138 and 140 is 2.

2. 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.

3. What are the Factors of 140?

Answer: Factors of 140 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140. There are 12 integers that are factors of 140. The greatest factor of 140 is 140.

4. How to Find the GCF of 138 and 140?

Answer:

Greatest Common Factor of 138 and 140 = 2

Step 1: Find the prime factorization of 138

138 = 2 x 3 x 23

Step 2: Find the prime factorization of 140

140 = 2 x 2 x 5 x 7

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 138 and 140 is 2