Greatest Common Factor of 119 and 126
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 119, 126 i.e. 7 largest integer by which both the numbers can be divided.
Greatest common factor (GCF) of 119 and 126 is 7.
GCF(119,126) = 7
GCF of 119 and 126
Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;
- Greatest Common Factor of 119 and 126 by prime factorization method
- Greatest Common Factor of 119 and 126 by matching factors method
GCF of 119 and 126 is 7
Prime Factorization of 119
| 7 | 119 |
| 17 | 17 |
| 1 |
Prime factors of 119 are 7,17. Prime factorization of 119 in exponential form is:
119 = 71×171
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
∴ So by taking common prime factors GCF of 119 and 126 is 7
Greatest Common Factor of 119 and 126 by matching factors method
Factors of 119
List of positive integer factors of 119 that divides 119 without a remainder.
1,7,17,119
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
Greatest Common Factor
We found the factors and prime factorization of 119 and 126. The biggest common factor number is the GCF number.
So the greatest common factor 119 and 126 is 7.
Also check out the Least Common Multiple of 119 and 126
Properties of GCF 119 and 126
(i) The GCF of 119 and 126 is associative
GCF of 119 and 126 = GCF of 126 and 119
Related Greatest Common Factor of 119
Related Greatest Common Factor of 126
Frequently Asked Questions on GCF of 119 and 126
1. What is the GCF of 119 and 126?
Answer: GCF of 119 and 126 is 7.
2. What are the Factors of 119?
Answer: Factors of 119 are 1, 7, 17, 119. There are 4 integers that are factors of 119. The greatest factor of 119 is 119.
3. 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.
4. How to Find the GCF of 119 and 126?
Answer:
Greatest Common Factor of 119 and 126 = 7
Step 1: Find the prime factorization of 119
119 = 7 x 17
Step 2: Find the prime factorization of 126
126 = 2 x 3 x 3 x 7
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 119 and 126 is 7
