Greatest Common Factor of 1900 and 1908

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 1900, 1908 i.e. 4 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 1900 and 1908 is 4.

GCF(1900,1908) = 4

GCF of 1900 and 1908

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

GCF of:
and

Greatest Common Factor of 1900 and 1908

GCF of 1900 and 1908 is 4

Prime Factorization of 1900


2 1900
2 950
5 475
5 95
19 19
1

Prime factors of 1900 are 2,5,19. Prime factorization of 1900 in exponential form is:

1900 = 22×52×191

Prime Factorization of 1908


2 1908
2 954
3 477
3 159
53 53
1

Prime factors of 1908 are 2,3,53. Prime factorization of 1908 in exponential form is:

1908 = 22×32×531

∴ So by taking common prime factors GCF of 1900 and 1908 is 4

Greatest Common Factor of 1900 and 1908 by matching factors method

Factors of 1900

List of positive integer factors of 1900 that divides 1900 without a remainder.

1,2,4,5,10,19,20,25,38,50,76,95,100,190,380,475,950,1900

Factors of 1908

List of positive integer factors of 1908 that divides 1908 without a remainder.

1,2,3,4,6,9,12,18,36,53,106,159,212,318,477,636,954,1908

Greatest Common Factor

We found the factors and prime factorization of 1900 and 1908. The biggest common factor number is the GCF number.
So the greatest common factor 1900 and 1908 is 4.

Also check out the Least Common Multiple of 1900 and 1908

Properties of GCF 1900 and 1908

(i) The GCF of 1900 and 1908 is associative

GCF of 1900 and 1908 = GCF of 1908 and 1900

Related Greatest Common Factor of 1900

Related Greatest Common Factor of 1908

Frequently Asked Questions on GCF of 1900 and 1908

1. What is the GCF of 1900 and 1908?

Answer: GCF of 1900 and 1908 is 4.

2. What are the Factors of 1900?

Answer: Factors of 1900 are 1, 2, 4, 5, 10, 19, 20, 25, 38, 50, 76, 95, 100, 190, 380, 475, 950, 1900. There are 18 integers that are factors of 1900. The greatest factor of 1900 is 1900.

3. What are the Factors of 1908?

Answer: Factors of 1908 are 1, 2, 3, 4, 6, 9, 12, 18, 36, 53, 106, 159, 212, 318, 477, 636, 954, 1908. There are 18 integers that are factors of 1908. The greatest factor of 1908 is 1908.

4. How to Find the GCF of 1900 and 1908?

Answer:

Greatest Common Factor of 1900 and 1908 = 4

Step 1: Find the prime factorization of 1900

1900 = 2 x 2 x 5 x 5 x 19

Step 2: Find the prime factorization of 1908

1908 = 2 x 2 x 3 x 3 x 53

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 1900 and 1908 is 4