Greatest Common Factor of 400 and 404

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

Greatest common factor (GCF) of 400 and 404 is 4.

GCF(400,404) = 4

GCF of 400 and 404

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

GCF of:
and

Greatest Common Factor of 400 and 404

GCF of 400 and 404 is 4

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 404


2 404
2 202
101 101
1

Prime factors of 404 are 2,101. Prime factorization of 404 in exponential form is:

404 = 22×1011

∴ So by taking common prime factors GCF of 400 and 404 is 4

Greatest Common Factor of 400 and 404 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 404

List of positive integer factors of 404 that divides 404 without a remainder.

1,2,4,101,202,404

Greatest Common Factor

We found the factors and prime factorization of 400 and 404. The biggest common factor number is the GCF number.
So the greatest common factor 400 and 404 is 4.

Also check out the Least Common Multiple of 400 and 404

Properties of GCF 400 and 404

(i) The GCF of 400 and 404 is associative

GCF of 400 and 404 = GCF of 404 and 400

Related Greatest Common Factor of 400

Related Greatest Common Factor of 404

Frequently Asked Questions on GCF of 400 and 404

1. What is the GCF of 400 and 404?

Answer: GCF of 400 and 404 is 4.

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 404?

Answer: Factors of 404 are 1, 2, 4, 101, 202, 404. There are 6 integers that are factors of 404. The greatest factor of 404 is 404.

4. How to Find the GCF of 400 and 404?

Answer:

Greatest Common Factor of 400 and 404 = 4

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 404

404 = 2 x 2 x 101

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 400 and 404 is 4