Greatest Common Factor of 2100 and 2105

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, 2105 i.e. 5 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 2100 and 2105 is 5.

GCF(2100,2105) = 5

GCF of 2100 and 2105

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

GCF of:
and

Greatest Common Factor of 2100 and 2105

GCF of 2100 and 2105 is 5

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 2105


5 2105
421 421
1

Prime factors of 2105 are 5,421. Prime factorization of 2105 in exponential form is:

2105 = 51×4211

∴ So by taking common prime factors GCF of 2100 and 2105 is 5

Greatest Common Factor of 2100 and 2105 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 2105

List of positive integer factors of 2105 that divides 2105 without a remainder.

1,5,421,2105

Greatest Common Factor

We found the factors and prime factorization of 2100 and 2105. The biggest common factor number is the GCF number.
So the greatest common factor 2100 and 2105 is 5.

Also check out the Least Common Multiple of 2100 and 2105

Properties of GCF 2100 and 2105

(i) The GCF of 2100 and 2105 is associative

GCF of 2100 and 2105 = GCF of 2105 and 2100

Related Greatest Common Factor of 2100

Related Greatest Common Factor of 2105

Frequently Asked Questions on GCF of 2100 and 2105

1. What is the GCF of 2100 and 2105?

Answer: GCF of 2100 and 2105 is 5.

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 2105?

Answer: Factors of 2105 are 1, 5, 421, 2105. There are 4 integers that are factors of 2105. The greatest factor of 2105 is 2105.

4. How to Find the GCF of 2100 and 2105?

Answer:

Greatest Common Factor of 2100 and 2105 = 5

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 2105

2105 = 5 x 421

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 2100 and 2105 is 5