Greatest Common Factor of 1900 and 1905

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, 1905 i.e. 5 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 1900 and 1905 is 5.

GCF(1900,1905) = 5

GCF of 1900 and 1905

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

GCF of:
and

Greatest Common Factor of 1900 and 1905

GCF of 1900 and 1905 is 5

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 1905


3 1905
5 635
127 127
1

Prime factors of 1905 are 3,5,127. Prime factorization of 1905 in exponential form is:

1905 = 31×51×1271

∴ So by taking common prime factors GCF of 1900 and 1905 is 5

Greatest Common Factor of 1900 and 1905 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 1905

List of positive integer factors of 1905 that divides 1905 without a remainder.

1,3,5,15,127,381,635,1905

Greatest Common Factor

We found the factors and prime factorization of 1900 and 1905. The biggest common factor number is the GCF number.
So the greatest common factor 1900 and 1905 is 5.

Also check out the Least Common Multiple of 1900 and 1905

Properties of GCF 1900 and 1905

(i) The GCF of 1900 and 1905 is associative

GCF of 1900 and 1905 = GCF of 1905 and 1900

Related Greatest Common Factor of 1900

Related Greatest Common Factor of 1905

Frequently Asked Questions on GCF of 1900 and 1905

1. What is the GCF of 1900 and 1905?

Answer: GCF of 1900 and 1905 is 5.

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 1905?

Answer: Factors of 1905 are 1, 3, 5, 15, 127, 381, 635, 1905. There are 8 integers that are factors of 1905. The greatest factor of 1905 is 1905.

4. How to Find the GCF of 1900 and 1905?

Answer:

Greatest Common Factor of 1900 and 1905 = 5

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 1905

1905 = 3 x 5 x 127

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

GCF = 5

Step 4: Therefore, the greatest common factor of 1900 and 1905 is 5