Greatest Common Factor of 138 and 144

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, 144 i.e. 6 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 138 and 144 is 6.

GCF(138,144) = 6

GCF of 138 and 144

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

GCF of:
and

Greatest Common Factor of 138 and 144

GCF of 138 and 144 is 6

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 144


2 144
2 72
2 36
2 18
3 9
3 3
1

Prime factors of 144 are 2,3. Prime factorization of 144 in exponential form is:

144 = 24×32

∴ So by taking common prime factors GCF of 138 and 144 is 6

Greatest Common Factor of 138 and 144 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 144

List of positive integer factors of 144 that divides 144 without a remainder.

1,2,3,4,6,8,9,12,16,18,24,36,48,72,144

Greatest Common Factor

We found the factors and prime factorization of 138 and 144. The biggest common factor number is the GCF number.
So the greatest common factor 138 and 144 is 6.

Also check out the Least Common Multiple of 138 and 144

Properties of GCF 138 and 144

(i) The GCF of 138 and 144 is associative

GCF of 138 and 144 = GCF of 144 and 138

Related Greatest Common Factor of 138

Related Greatest Common Factor of 144

Frequently Asked Questions on GCF of 138 and 144

1. What is the GCF of 138 and 144?

Answer: GCF of 138 and 144 is 6.

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 144?

Answer: Factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144. There are 15 integers that are factors of 144. The greatest factor of 144 is 144.

4. How to Find the GCF of 138 and 144?

Answer:

Greatest Common Factor of 138 and 144 = 6

Step 1: Find the prime factorization of 138

138 = 2 x 3 x 23

Step 2: Find the prime factorization of 144

144 = 2 x 2 x 2 x 2 x 3 x 3

Step 3: Multiply those factors both numbers have in common in steps i) or ii) above to find the gcf:

GCF = 2 x 3 = 6

Step 4: Therefore, the greatest common factor of 138 and 144 is 6