Greatest Common Factor of 400 and 420

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 400, 420 i.e. 20 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 400 and 420 is 20.

GCF(400,420) = 20

GCF of 400 and 420

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

GCF of:
and

Greatest Common Factor of 400 and 420

GCF of 400 and 420 is 20

Prime Factorization of 400


2 400
2 200
2 100
2 50
5 25
5 5
1

Prime factors of 400 are 2,5. Prime factorization of 400 in exponential form is:

400 = 24×52

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

∴ So by taking common prime factors GCF of 400 and 420 is 20

Greatest Common Factor of 400 and 420 by matching factors method

Factors of 400

List of positive integer factors of 400 that divides 400 without a remainder.

1,2,4,5,8,10,16,20,25,40,50,80,100,200,400

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

Greatest Common Factor

We found the factors and prime factorization of 400 and 420. The biggest common factor number is the GCF number.
So the greatest common factor 400 and 420 is 20.

Also check out the Least Common Multiple of 400 and 420

Properties of GCF 400 and 420

(i) The GCF of 400 and 420 is associative

GCF of 400 and 420 = GCF of 420 and 400

Related Greatest Common Factor of 400

Related Greatest Common Factor of 420

Frequently Asked Questions on GCF of 400 and 420

1. What is the GCF of 400 and 420?

Answer: GCF of 400 and 420 is 20.

2. What are the Factors of 400?

Answer: Factors of 400 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400. There are 15 integers that are factors of 400. The greatest factor of 400 is 400.

3. 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.

4. How to Find the GCF of 400 and 420?

Answer:

Greatest Common Factor of 400 and 420 = 20

Step 1: Find the prime factorization of 400

400 = 2 x 2 x 2 x 2 x 5 x 5

Step 2: Find the prime factorization of 420

420 = 2 x 2 x 3 x 5 x 7

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

GCF = 2 x 2 x 5 = 20

Step 4: Therefore, the greatest common factor of 400 and 420 is 20