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;
- Greatest Common Factor of 126 and 133 by prime factorization method
- Greatest Common Factor of 126 and 133 by matching factors method
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
