Greatest Common Factor of 126 and 132

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 126, 132 i.e. 6 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 126 and 132 is 6.

GCF(126,132) = 6

GCF of 126 and 132

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

GCF of:
and

Greatest Common Factor of 126 and 132

GCF of 126 and 132 is 6

Prime Factorization of 126


2 126
3 63
3 21
7 7
1

Prime factors of 126 are 2,3,7. Prime factorization of 126 in exponential form is:

126 = 21×32×71

Prime Factorization of 132


2 132
2 66
3 33
11 11
1

Prime factors of 132 are 2,3,11. Prime factorization of 132 in exponential form is:

132 = 22×31×111

∴ So by taking common prime factors GCF of 126 and 132 is 6

Greatest Common Factor of 126 and 132 by matching factors method

Factors of 126

List of positive integer factors of 126 that divides 126 without a remainder.

1,2,3,6,7,9,14,18,21,42,63,126

Factors of 132

List of positive integer factors of 132 that divides 132 without a remainder.

1,2,3,4,6,11,12,22,33,44,66,132

Greatest Common Factor

We found the factors and prime factorization of 126 and 132. The biggest common factor number is the GCF number.
So the greatest common factor 126 and 132 is 6.

Also check out the Least Common Multiple of 126 and 132

Properties of GCF 126 and 132

(i) The GCF of 126 and 132 is associative

GCF of 126 and 132 = GCF of 132 and 126

Related Greatest Common Factor of 126

Related Greatest Common Factor of 132

Frequently Asked Questions on GCF of 126 and 132

1. What is the GCF of 126 and 132?

Answer: GCF of 126 and 132 is 6.

2. What are the Factors of 126?

Answer: Factors of 126 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126. There are 12 integers that are factors of 126. The greatest factor of 126 is 126.

3. What are the Factors of 132?

Answer: Factors of 132 are 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132. There are 12 integers that are factors of 132. The greatest factor of 132 is 132.

4. How to Find the GCF of 126 and 132?

Answer:

Greatest Common Factor of 126 and 132 = 6

Step 1: Find the prime factorization of 126

126 = 2 x 3 x 3 x 7

Step 2: Find the prime factorization of 132

132 = 2 x 2 x 3 x 11

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 126 and 132 is 6