Greatest Common Factor of 42 and 63
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, 63 i.e. 21 largest integer by which both the numbers can be divided.
Greatest common factor (GCF) of 42 and 63 is 21.
GCF(42,63) = 21
GCF of 42 and 63
Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;
- Greatest Common Factor of 42 and 63 by prime factorization method
- Greatest Common Factor of 42 and 63 by matching factors method
GCF of 42 and 63 is 21
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 63
| 3 | 63 |
| 3 | 21 |
| 7 | 7 |
| 1 |
Prime factors of 63 are 3,7. Prime factorization of 63 in exponential form is:
63 = 32×71
∴ So by taking common prime factors GCF of 42 and 63 is 21
Greatest Common Factor of 42 and 63 by matching factors method
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 63
List of positive integer factors of 63 that divides 63 without a remainder.
1,3,7,9,21,63
Greatest Common Factor
We found the factors and prime factorization of 42 and 63. The biggest common factor number is the GCF number.
So the greatest common factor 42 and 63 is 21.
Also check out the Least Common Multiple of 42 and 63
Properties of GCF 42 and 63
(i) The GCF of 42 and 63 is associative
GCF of 42 and 63 = GCF of 63 and 42
Related Greatest Common Factor of 42
Related Greatest Common Factor of 63
Frequently Asked Questions on GCF of 42 and 63
1. What is the GCF of 42 and 63?
Answer: GCF of 42 and 63 is 21.
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 63?
Answer: Factors of 63 are 1, 3, 7, 9, 21, 63. There are 6 integers that are factors of 63. The greatest factor of 63 is 63.
4. How to Find the GCF of 42 and 63?
Answer:
Greatest Common Factor of 42 and 63 = 21
Step 1: Find the prime factorization of 42
42 = 2 x 3 x 7
Step 2: Find the prime factorization of 63
63 = 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 = 3 x 7 = 21
Step 4: Therefore, the greatest common factor of 42 and 63 is 21