Greatest Common Factor of 126 and 133

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, 133 i.e. 7 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 126 and 133 is 7.

GCF(126,133) = 7

GCF of 126 and 133

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

GCF of:
and

Greatest Common Factor of 126 and 133

GCF of 126 and 133 is 7

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 133


7 133
19 19
1

Prime factors of 133 are 7,19. Prime factorization of 133 in exponential form is:

133 = 71×191

∴ So by taking common prime factors GCF of 126 and 133 is 7

Greatest Common Factor of 126 and 133 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 133

List of positive integer factors of 133 that divides 133 without a remainder.

1,7,19,133

Greatest Common Factor

We found the factors and prime factorization of 126 and 133. The biggest common factor number is the GCF number.
So the greatest common factor 126 and 133 is 7.

Also check out the Least Common Multiple of 126 and 133

Properties of GCF 126 and 133

(i) The GCF of 126 and 133 is associative

GCF of 126 and 133 = GCF of 133 and 126

Related Greatest Common Factor of 126

Related Greatest Common Factor of 133

Frequently Asked Questions on GCF of 126 and 133

1. What is the GCF of 126 and 133?

Answer: GCF of 126 and 133 is 7.

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 133?

Answer: Factors of 133 are 1, 7, 19, 133. There are 4 integers that are factors of 133. The greatest factor of 133 is 133.

4. How to Find the GCF of 126 and 133?

Answer:

Greatest Common Factor of 126 and 133 = 7

Step 1: Find the prime factorization of 126

126 = 2 x 3 x 3 x 7

Step 2: Find the prime factorization of 133

133 = 7 x 19

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

GCF = 7

Step 4: Therefore, the greatest common factor of 126 and 133 is 7