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 42, 51 i.e. 3 largest integer by which both the numbers can be divided.
Greatest common factor (GCF) of 42 and 51 is 3.
GCF(42,51) = 3
Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;
Prime Factorization of 42
2 | 42 |
3 | 21 |
7 | 7 |
1 |
Prime factors of 42 are 2,3,7. Prime factorization of 42 in exponential form is:
42 = 21×31×71
Prime Factorization of 51
3 | 51 |
17 | 17 |
1 |
Prime factors of 51 are 3,17. Prime factorization of 51 in exponential form is:
51 = 31×171
∴ So by taking common prime factors GCF of 42 and 51 is 3
Factors of 42
List of positive integer factors of 42 that divides 42 without a remainder.
1,2,3,6,7,14,21,42
Factors of 51
List of positive integer factors of 51 that divides 51 without a remainder.
1,3,17,51
Greatest Common Factor
We found the factors and prime factorization of 42 and 51. The biggest common factor number is the GCF number.
So the greatest common factor 42 and 51 is 3.
Also check out the Least Common Multiple of 42 and 51
(i) The GCF of 42 and 51 is associative
GCF of 42 and 51 = GCF of 51 and 42
1. What is the GCF of 42 and 51?
Answer: GCF of 42 and 51 is 3.
2. What are the Factors of 42?
Answer: Factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42. There are 8 integers that are factors of 42. The greatest factor of 42 is 42.
3. What are the Factors of 51?
Answer: Factors of 51 are 1, 3, 17, 51. There are 4 integers that are factors of 51. The greatest factor of 51 is 51.
4. How to Find the GCF of 42 and 51?
Answer:
Greatest Common Factor of 42 and 51 = 3
Step 1: Find the prime factorization of 42
42 = 2 x 3 x 7
Step 2: Find the prime factorization of 51
51 = 3 x 17
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 42 and 51 is 3