Greatest Common Factor of 2100 and 2108

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 2100, 2108 i.e. 4 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 2100 and 2108 is 4.

GCF(2100,2108) = 4

GCF of 2100 and 2108

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

GCF of:
and

Greatest Common Factor of 2100 and 2108

GCF of 2100 and 2108 is 4

Prime Factorization of 2100


2 2100
2 1050
3 525
5 175
5 35
7 7
1

Prime factors of 2100 are 2,3,5,7. Prime factorization of 2100 in exponential form is:

2100 = 22×31×52×71

Prime Factorization of 2108


2 2108
2 1054
17 527
31 31
1

Prime factors of 2108 are 2,17,31. Prime factorization of 2108 in exponential form is:

2108 = 22×171×311

∴ So by taking common prime factors GCF of 2100 and 2108 is 4

Greatest Common Factor of 2100 and 2108 by matching factors method

Factors of 2100

List of positive integer factors of 2100 that divides 2100 without a remainder.

1,2,3,4,5,6,7,10,12,14,15,20,21,25,28,30,35,42,50,60,70,75,84,100,105,140,150,175,210,300,350,420,525,700,1050,2100

Factors of 2108

List of positive integer factors of 2108 that divides 2108 without a remainder.

1,2,4,17,31,34,62,68,124,527,1054,2108

Greatest Common Factor

We found the factors and prime factorization of 2100 and 2108. The biggest common factor number is the GCF number.
So the greatest common factor 2100 and 2108 is 4.

Also check out the Least Common Multiple of 2100 and 2108

Properties of GCF 2100 and 2108

(i) The GCF of 2100 and 2108 is associative

GCF of 2100 and 2108 = GCF of 2108 and 2100

Related Greatest Common Factor of 2100

Related Greatest Common Factor of 2108

Frequently Asked Questions on GCF of 2100 and 2108

1. What is the GCF of 2100 and 2108?

Answer: GCF of 2100 and 2108 is 4.

2. What are the Factors of 2100?

Answer: Factors of 2100 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 25, 28, 30, 35, 42, 50, 60, 70, 75, 84, 100, 105, 140, 150, 175, 210, 300, 350, 420, 525, 700, 1050, 2100. There are 36 integers that are factors of 2100. The greatest factor of 2100 is 2100.

3. What are the Factors of 2108?

Answer: Factors of 2108 are 1, 2, 4, 17, 31, 34, 62, 68, 124, 527, 1054, 2108. There are 12 integers that are factors of 2108. The greatest factor of 2108 is 2108.

4. How to Find the GCF of 2100 and 2108?

Answer:

Greatest Common Factor of 2100 and 2108 = 4

Step 1: Find the prime factorization of 2100

2100 = 2 x 2 x 3 x 5 x 5 x 7

Step 2: Find the prime factorization of 2108

2108 = 2 x 2 x 17 x 31

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 2100 and 2108 is 4