Greatest Common Factor of 100 and 106

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

Greatest common factor (GCF) of 100 and 106 is 2.

GCF(100,106) = 2

GCF of 100 and 106

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

GCF of:
and

Greatest Common Factor of 100 and 106

GCF of 100 and 106 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 106


2 106
53 53
1

Prime factors of 106 are 2,53. Prime factorization of 106 in exponential form is:

106 = 21×531

∴ So by taking common prime factors GCF of 100 and 106 is 2

Greatest Common Factor of 100 and 106 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 106

List of positive integer factors of 106 that divides 106 without a remainder.

1,2,53,106

Greatest Common Factor

We found the factors and prime factorization of 100 and 106. The biggest common factor number is the GCF number.
So the greatest common factor 100 and 106 is 2.

Also check out the Least Common Multiple of 100 and 106

Properties of GCF 100 and 106

(i) The GCF of 100 and 106 is associative

GCF of 100 and 106 = GCF of 106 and 100

Related Greatest Common Factor of 100

Related Greatest Common Factor of 106

Frequently Asked Questions on GCF of 100 and 106

1. What is the GCF of 100 and 106?

Answer: GCF of 100 and 106 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 106?

Answer: Factors of 106 are 1, 2, 53, 106. There are 4 integers that are factors of 106. The greatest factor of 106 is 106.

4. How to Find the GCF of 100 and 106?

Answer:

Greatest Common Factor of 100 and 106 = 2

Step 1: Find the prime factorization of 100

100 = 2 x 2 x 5 x 5

Step 2: Find the prime factorization of 106

106 = 2 x 53

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 106 is 2