Greatest Common Factor of 126 and 129

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

Greatest common factor (GCF) of 126 and 129 is 3.

GCF(126,129) = 3

GCF of 126 and 129

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

GCF of:
and

Greatest Common Factor of 126 and 129

GCF of 126 and 129 is 3

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 129


3 129
43 43
1

Prime factors of 129 are 3,43. Prime factorization of 129 in exponential form is:

129 = 31×431

∴ So by taking common prime factors GCF of 126 and 129 is 3

Greatest Common Factor of 126 and 129 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 129

List of positive integer factors of 129 that divides 129 without a remainder.

1,3,43,129

Greatest Common Factor

We found the factors and prime factorization of 126 and 129. The biggest common factor number is the GCF number.
So the greatest common factor 126 and 129 is 3.

Also check out the Least Common Multiple of 126 and 129

Properties of GCF 126 and 129

(i) The GCF of 126 and 129 is associative

GCF of 126 and 129 = GCF of 129 and 126

Related Greatest Common Factor of 126

Related Greatest Common Factor of 129

Frequently Asked Questions on GCF of 126 and 129

1. What is the GCF of 126 and 129?

Answer: GCF of 126 and 129 is 3.

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 129?

Answer: Factors of 129 are 1, 3, 43, 129. There are 4 integers that are factors of 129. The greatest factor of 129 is 129.

4. How to Find the GCF of 126 and 129?

Answer:

Greatest Common Factor of 126 and 129 = 3

Step 1: Find the prime factorization of 126

126 = 2 x 3 x 3 x 7

Step 2: Find the prime factorization of 129

129 = 3 x 43

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 126 and 129 is 3