Greatest Common Factor of 420 and 423

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, 423 i.e. 3 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 420 and 423 is 3.

GCF(420,423) = 3

GCF of 420 and 423

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

GCF of:
and

Greatest Common Factor of 420 and 423

GCF of 420 and 423 is 3

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 423


3 423
3 141
47 47
1

Prime factors of 423 are 3,47. Prime factorization of 423 in exponential form is:

423 = 32×471

∴ So by taking common prime factors GCF of 420 and 423 is 3

Greatest Common Factor of 420 and 423 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 423

List of positive integer factors of 423 that divides 423 without a remainder.

1,3,9,47,141,423

Greatest Common Factor

We found the factors and prime factorization of 420 and 423. The biggest common factor number is the GCF number.
So the greatest common factor 420 and 423 is 3.

Also check out the Least Common Multiple of 420 and 423

Properties of GCF 420 and 423

(i) The GCF of 420 and 423 is associative

GCF of 420 and 423 = GCF of 423 and 420

Related Greatest Common Factor of 420

Related Greatest Common Factor of 423

Frequently Asked Questions on GCF of 420 and 423

1. What is the GCF of 420 and 423?

Answer: GCF of 420 and 423 is 3.

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 423?

Answer: Factors of 423 are 1, 3, 9, 47, 141, 423. There are 6 integers that are factors of 423. The greatest factor of 423 is 423.

4. How to Find the GCF of 420 and 423?

Answer:

Greatest Common Factor of 420 and 423 = 3

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 423

423 = 3 x 3 x 47

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

GCF = 3

Step 4: Therefore, the greatest common factor of 420 and 423 is 3