Greatest Common Factor of 1896 and 1900

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 1896, 1900 i.e. 4 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 1896 and 1900 is 4.

GCF(1896,1900) = 4

GCF of 1896 and 1900

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

GCF of:
and

Greatest Common Factor of 1896 and 1900

GCF of 1896 and 1900 is 4

Prime Factorization of 1896


2 1896
2 948
2 474
3 237
79 79
1

Prime factors of 1896 are 2,3,79. Prime factorization of 1896 in exponential form is:

1896 = 23×31×791

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

∴ So by taking common prime factors GCF of 1896 and 1900 is 4

Greatest Common Factor of 1896 and 1900 by matching factors method

Factors of 1896

List of positive integer factors of 1896 that divides 1896 without a remainder.

1,2,3,4,6,8,12,24,79,158,237,316,474,632,948,1896

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

Greatest Common Factor

We found the factors and prime factorization of 1896 and 1900. The biggest common factor number is the GCF number.
So the greatest common factor 1896 and 1900 is 4.

Also check out the Least Common Multiple of 1896 and 1900

Properties of GCF 1896 and 1900

(i) The GCF of 1896 and 1900 is associative

GCF of 1896 and 1900 = GCF of 1900 and 1896

Related Greatest Common Factor of 1896

Related Greatest Common Factor of 1900

Frequently Asked Questions on GCF of 1896 and 1900

1. What is the GCF of 1896 and 1900?

Answer: GCF of 1896 and 1900 is 4.

2. What are the Factors of 1896?

Answer: Factors of 1896 are 1, 2, 3, 4, 6, 8, 12, 24, 79, 158, 237, 316, 474, 632, 948, 1896. There are 16 integers that are factors of 1896. The greatest factor of 1896 is 1896.

3. 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.

4. How to Find the GCF of 1896 and 1900?

Answer:

Greatest Common Factor of 1896 and 1900 = 4

Step 1: Find the prime factorization of 1896

1896 = 2 x 2 x 2 x 3 x 79

Step 2: Find the prime factorization of 1900

1900 = 2 x 2 x 5 x 5 x 19

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 1896 and 1900 is 4