# Greatest Common Factor of 420 and 422

Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 420, 422 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 420 and 422 is 2.

GCF(420,422) = 2

## GCF of 420 and 422

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

GCF of:
and

### Greatest Common Factor of 420 and 422 by Prime factorization method

Prime Factorization of 420

 2 420 2 210 3 105 5 35 7 7 1

Prime factors of 420 are 2,3,5,7. Prime factorization of 420 in exponential form is:

420 = 22×31×51×71

Prime Factorization of 422

 2 422 211 211 1

Prime factors of 422 are 2,211. Prime factorization of 422 in exponential form is:

422 = 21×2111

∴ So by taking common prime factors GCF of 420 and 422 is 2

### Greatest Common Factor of 420 and 422 by matching factors method

Factors of 420

List of positive integer factors of 420 that divides 420 without a remainder.

1,2,3,4,5,6,7,10,12,14,15,20,21,28,30,35,42,60,70,84,105,140,210,420

Factors of 422

List of positive integer factors of 422 that divides 422 without a remainder.

1,2,211,422

Greatest Common Factor

We found the factors and prime factorization of 420 and 422. The biggest common factor number is the GCF number.
So the greatest common factor 420 and 422 is 2.

Also check out the Least Common Multiple of 420 and 422

### Properties of GCF 420 and 422

(i) The GCF of 420 and 422 is associative

GCF of 420 and 422 = GCF of 422 and 420

### Frequently Asked Questions on GCF of 420 and 422

1. What is the GCF of 420 and 422?

Answer: GCF of 420 and 422 is 2.

2. What are the Factors of 420?

Answer: Factors of 420 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420. There are 24 integers that are factors of 420. The greatest factor of 420 is 420.

3. What are the Factors of 422?

Answer: Factors of 422 are 1, 2, 211, 422. There are 4 integers that are factors of 422. The greatest factor of 422 is 422.

4. How to Find the GCF of 420 and 422?

Greatest Common Factor of 420 and 422 = 2

Step 1: Find the prime factorization of 420

420 = 2 x 2 x 3 x 5 x 7

Step 2: Find the prime factorization of 422

422 = 2 x 211

Step 3: Multiply those factors both numbers have in common in steps i) or ii) above to find the gcf:

GCF = 2

Step 4: Therefore, the greatest common factor of 420 and 422 is 2