Greatest Common Factor of 1400 and 1404

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 1400, 1404 i.e. 4 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 1400 and 1404 is 4.

GCF(1400,1404) = 4

GCF of 1400 and 1404

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

GCF of:
and

Greatest Common Factor of 1400 and 1404

GCF of 1400 and 1404 is 4

Prime Factorization of 1400


2 1400
2 700
2 350
5 175
5 35
7 7
1

Prime factors of 1400 are 2,5,7. Prime factorization of 1400 in exponential form is:

1400 = 23×52×71

Prime Factorization of 1404


2 1404
2 702
3 351
3 117
3 39
13 13
1

Prime factors of 1404 are 2,3,13. Prime factorization of 1404 in exponential form is:

1404 = 22×33×131

∴ So by taking common prime factors GCF of 1400 and 1404 is 4

Greatest Common Factor of 1400 and 1404 by matching factors method

Factors of 1400

List of positive integer factors of 1400 that divides 1400 without a remainder.

1,2,4,5,7,8,10,14,20,25,28,35,40,50,56,70,100,140,175,200,280,350,700,1400

Factors of 1404

List of positive integer factors of 1404 that divides 1404 without a remainder.

1,2,3,4,6,9,12,13,18,26,27,36,39,52,54,78,108,117,156,234,351,468,702,1404

Greatest Common Factor

We found the factors and prime factorization of 1400 and 1404. The biggest common factor number is the GCF number.
So the greatest common factor 1400 and 1404 is 4.

Also check out the Least Common Multiple of 1400 and 1404

Properties of GCF 1400 and 1404

(i) The GCF of 1400 and 1404 is associative

GCF of 1400 and 1404 = GCF of 1404 and 1400

Related Greatest Common Factor of 1400

Related Greatest Common Factor of 1404

Frequently Asked Questions on GCF of 1400 and 1404

1. What is the GCF of 1400 and 1404?

Answer: GCF of 1400 and 1404 is 4.

2. What are the Factors of 1400?

Answer: Factors of 1400 are 1, 2, 4, 5, 7, 8, 10, 14, 20, 25, 28, 35, 40, 50, 56, 70, 100, 140, 175, 200, 280, 350, 700, 1400. There are 24 integers that are factors of 1400. The greatest factor of 1400 is 1400.

3. What are the Factors of 1404?

Answer: Factors of 1404 are 1, 2, 3, 4, 6, 9, 12, 13, 18, 26, 27, 36, 39, 52, 54, 78, 108, 117, 156, 234, 351, 468, 702, 1404. There are 24 integers that are factors of 1404. The greatest factor of 1404 is 1404.

4. How to Find the GCF of 1400 and 1404?

Answer:

Greatest Common Factor of 1400 and 1404 = 4

Step 1: Find the prime factorization of 1400

1400 = 2 x 2 x 2 x 5 x 5 x 7

Step 2: Find the prime factorization of 1404

1404 = 2 x 2 x 3 x 3 x 3 x 13

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 1400 and 1404 is 4