# Greatest Common Factor of 42 and 49

Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 42, 49 i.e. 7 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 42 and 49 is 7.

GCF(42,49) = 7

## GCF of 42 and 49

Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;

GCF of:
and

### Greatest Common Factor of 42 and 49 by Prime factorization method

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 49

 7 49 7 7 1

Prime factors of 49 are 7. Prime factorization of 49 in exponential form is:

49 = 72

∴ So by taking common prime factors GCF of 42 and 49 is 7

### Greatest Common Factor of 42 and 49 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 49

List of positive integer factors of 49 that divides 49 without a remainder.

1,7,49

Greatest Common Factor

We found the factors and prime factorization of 42 and 49. The biggest common factor number is the GCF number.
So the greatest common factor 42 and 49 is 7.

Also check out the Least Common Multiple of 42 and 49

### Properties of GCF 42 and 49

(i) The GCF of 42 and 49 is associative

GCF of 42 and 49 = GCF of 49 and 42

### Frequently Asked Questions on GCF of 42 and 49

1. What is the GCF of 42 and 49?

Answer: GCF of 42 and 49 is 7.

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 49?

Answer: Factors of 49 are 1, 7, 49. There are 3 integers that are factors of 49. The greatest factor of 49 is 49.

4. How to Find the GCF of 42 and 49?

Greatest Common Factor of 42 and 49 = 7

Step 1: Find the prime factorization of 42

42 = 2 x 3 x 7

Step 2: Find the prime factorization of 49

49 = 7 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 42 and 49 is 7