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 120, 126 i.e. 6 largest integer by which both the numbers can be divided.
Greatest common factor (GCF) of 120 and 126 is 6.
GCF(120,126) = 6
Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;
Prime Factorization of 120
2 | 120 |
2 | 60 |
2 | 30 |
3 | 15 |
5 | 5 |
1 |
Prime factors of 120 are 2,3,5. Prime factorization of 120 in exponential form is:
120 = 23×31×51
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 120 and 126 is 6
Factors of 120
List of positive integer factors of 120 that divides 120 without a remainder.
1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120
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 120 and 126. The biggest common factor number is the GCF number.
So the greatest common factor 120 and 126 is 6.
Also check out the Least Common Multiple of 120 and 126
(i) The GCF of 120 and 126 is associative
GCF of 120 and 126 = GCF of 126 and 120
1. What is the GCF of 120 and 126?
Answer: GCF of 120 and 126 is 6.
2. What are the Factors of 120?
Answer: Factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120. There are 16 integers that are factors of 120. The greatest factor of 120 is 120.
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 120 and 126?
Answer:
Greatest Common Factor of 120 and 126 = 6
Step 1: Find the prime factorization of 120
120 = 2 x 2 x 2 x 3 x 5
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 = 2 x 3 = 6
Step 4: Therefore, the greatest common factor of 120 and 126 is 6