Greatest Common Factor of 102 and 105

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 102, 105 i.e. 3 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 102 and 105 is 3.

GCF(102,105) = 3

GCF of 102 and 105

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

GCF of:
and

Greatest Common Factor of 102 and 105

GCF of 102 and 105 is 3

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

Prime Factorization of 105


3 105
5 35
7 7
1

Prime factors of 105 are 3,5,7. Prime factorization of 105 in exponential form is:

105 = 31×51×71

∴ So by taking common prime factors GCF of 102 and 105 is 3

Greatest Common Factor of 102 and 105 by matching factors method

Factors of 102

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

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

Factors of 105

List of positive integer factors of 105 that divides 105 without a remainder.

1,3,5,7,15,21,35,105

Greatest Common Factor

We found the factors and prime factorization of 102 and 105. The biggest common factor number is the GCF number.
So the greatest common factor 102 and 105 is 3.

Also check out the Least Common Multiple of 102 and 105

Properties of GCF 102 and 105

(i) The GCF of 102 and 105 is associative

GCF of 102 and 105 = GCF of 105 and 102

Related Greatest Common Factor of 102

Related Greatest Common Factor of 105

Frequently Asked Questions on GCF of 102 and 105

1. What is the GCF of 102 and 105?

Answer: GCF of 102 and 105 is 3.

2. 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.

3. What are the Factors of 105?

Answer: Factors of 105 are 1, 3, 5, 7, 15, 21, 35, 105. There are 8 integers that are factors of 105. The greatest factor of 105 is 105.

4. How to Find the GCF of 102 and 105?

Answer:

Greatest Common Factor of 102 and 105 = 3

Step 1: Find the prime factorization of 102

102 = 2 x 3 x 17

Step 2: Find the prime factorization of 105

105 = 3 x 5 x 7

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

GCF = 3

Step 4: Therefore, the greatest common factor of 102 and 105 is 3