Greatest Common Factor of 100 and 104

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

Greatest common factor (GCF) of 100 and 104 is 4.

GCF(100,104) = 4

GCF of 100 and 104

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

GCF of:
and

Greatest Common Factor of 100 and 104

GCF of 100 and 104 is 4

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 104


2 104
2 52
2 26
13 13
1

Prime factors of 104 are 2,13. Prime factorization of 104 in exponential form is:

104 = 23×131

∴ So by taking common prime factors GCF of 100 and 104 is 4

Greatest Common Factor of 100 and 104 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 104

List of positive integer factors of 104 that divides 104 without a remainder.

1,2,4,8,13,26,52,104

Greatest Common Factor

We found the factors and prime factorization of 100 and 104. The biggest common factor number is the GCF number.
So the greatest common factor 100 and 104 is 4.

Also check out the Least Common Multiple of 100 and 104

Properties of GCF 100 and 104

(i) The GCF of 100 and 104 is associative

GCF of 100 and 104 = GCF of 104 and 100

Related Greatest Common Factor of 100

Related Greatest Common Factor of 104

Frequently Asked Questions on GCF of 100 and 104

1. What is the GCF of 100 and 104?

Answer: GCF of 100 and 104 is 4.

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 104?

Answer: Factors of 104 are 1, 2, 4, 8, 13, 26, 52, 104. There are 8 integers that are factors of 104. The greatest factor of 104 is 104.

4. How to Find the GCF of 100 and 104?

Answer:

Greatest Common Factor of 100 and 104 = 4

Step 1: Find the prime factorization of 100

100 = 2 x 2 x 5 x 5

Step 2: Find the prime factorization of 104

104 = 2 x 2 x 2 x 13

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 100 and 104 is 4