Greatest Common Factor of 420 and 428

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 420, 428 i.e. 4 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 420 and 428 is 4.

GCF(420,428) = 4

GCF of 420 and 428

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

GCF of:
and

Greatest Common Factor of 420 and 428

GCF of 420 and 428 is 4

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 428


2 428
2 214
107 107
1

Prime factors of 428 are 2,107. Prime factorization of 428 in exponential form is:

428 = 22×1071

∴ So by taking common prime factors GCF of 420 and 428 is 4

Greatest Common Factor of 420 and 428 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 428

List of positive integer factors of 428 that divides 428 without a remainder.

1,2,4,107,214,428

Greatest Common Factor

We found the factors and prime factorization of 420 and 428. The biggest common factor number is the GCF number.
So the greatest common factor 420 and 428 is 4.

Also check out the Least Common Multiple of 420 and 428

Properties of GCF 420 and 428

(i) The GCF of 420 and 428 is associative

GCF of 420 and 428 = GCF of 428 and 420

Related Greatest Common Factor of 420

Related Greatest Common Factor of 428

Frequently Asked Questions on GCF of 420 and 428

1. What is the GCF of 420 and 428?

Answer: GCF of 420 and 428 is 4.

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 428?

Answer: Factors of 428 are 1, 2, 4, 107, 214, 428. There are 6 integers that are factors of 428. The greatest factor of 428 is 428.

4. How to Find the GCF of 420 and 428?

Answer:

Greatest Common Factor of 420 and 428 = 4

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 428

428 = 2 x 2 x 107

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

GCF = 2 x 2 = 4

Step 4: Therefore, the greatest common factor of 420 and 428 is 4