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, 48 i.e. 6 largest integer by which both the numbers can be divided.
Greatest common factor (GCF) of 42 and 48 is 6.
GCF(42,48) = 6
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 48
2 | 48 |
2 | 24 |
2 | 12 |
2 | 6 |
3 | 3 |
1 |
Prime factors of 48 are 2,3. Prime factorization of 48 in exponential form is:
48 = 24×31
∴ So by taking common prime factors GCF of 42 and 48 is 6
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 48
List of positive integer factors of 48 that divides 48 without a remainder.
1,2,3,4,6,8,12,16,24,48
Greatest Common Factor
We found the factors and prime factorization of 42 and 48. The biggest common factor number is the GCF number.
So the greatest common factor 42 and 48 is 6.
Also check out the Least Common Multiple of 42 and 48
(i) The GCF of 42 and 48 is associative
GCF of 42 and 48 = GCF of 48 and 42
1. What is the GCF of 42 and 48?
Answer: GCF of 42 and 48 is 6.
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 48?
Answer: Factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. There are 10 integers that are factors of 48. The greatest factor of 48 is 48.
4. How to Find the GCF of 42 and 48?
Answer:
Greatest Common Factor of 42 and 48 = 6
Step 1: Find the prime factorization of 42
42 = 2 x 3 x 7
Step 2: Find the prime factorization of 48
48 = 2 x 2 x 2 x 2 x 3
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 42 and 48 is 6