Greatest Common Factor of 100 and 102

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 100, 102 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 100 and 102 is 2.

GCF(100,102) = 2

GCF of 100 and 102

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

GCF of:
and

Greatest Common Factor of 100 and 102

GCF of 100 and 102 is 2

Prime Factorization of 100


2 100
2 50
5 25
5 5
1

Prime factors of 100 are 2,5. Prime factorization of 100 in exponential form is:

100 = 22×52

Prime Factorization of 102


2 102
3 51
17 17
1

Prime factors of 102 are 2,3,17. Prime factorization of 102 in exponential form is:

102 = 21×31×171

∴ So by taking common prime factors GCF of 100 and 102 is 2

Greatest Common Factor of 100 and 102 by matching factors method

Factors of 100

List of positive integer factors of 100 that divides 100 without a remainder.

1,2,4,5,10,20,25,50,100

Factors of 102

List of positive integer factors of 102 that divides 102 without a remainder.

1,2,3,6,17,34,51,102

Greatest Common Factor

We found the factors and prime factorization of 100 and 102. The biggest common factor number is the GCF number.
So the greatest common factor 100 and 102 is 2.

Also check out the Least Common Multiple of 100 and 102

Properties of GCF 100 and 102

(i) The GCF of 100 and 102 is associative

GCF of 100 and 102 = GCF of 102 and 100

Related Greatest Common Factor of 100

Related Greatest Common Factor of 102

Frequently Asked Questions on GCF of 100 and 102

1. What is the GCF of 100 and 102?

Answer: GCF of 100 and 102 is 2.

2. What are the Factors of 100?

Answer: Factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, 100. There are 9 integers that are factors of 100. The greatest factor of 100 is 100.

3. What are the Factors of 102?

Answer: Factors of 102 are 1, 2, 3, 6, 17, 34, 51, 102. There are 8 integers that are factors of 102. The greatest factor of 102 is 102.

4. How to Find the GCF of 100 and 102?

Answer:

Greatest Common Factor of 100 and 102 = 2

Step 1: Find the prime factorization of 100

100 = 2 x 2 x 5 x 5

Step 2: Find the prime factorization of 102

102 = 2 x 3 x 17

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

GCF = 2

Step 4: Therefore, the greatest common factor of 100 and 102 is 2