Greatest Common Factor of 105 and 111

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 105, 111 i.e. 3 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 105 and 111 is 3.

GCF(105,111) = 3

GCF of 105 and 111

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

GCF of:
and

Greatest Common Factor of 105 and 111

GCF of 105 and 111 is 3

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

Prime Factorization of 111


3 111
37 37
1

Prime factors of 111 are 3,37. Prime factorization of 111 in exponential form is:

111 = 31×371

∴ So by taking common prime factors GCF of 105 and 111 is 3

Greatest Common Factor of 105 and 111 by matching factors method

Factors of 105

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

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

Factors of 111

List of positive integer factors of 111 that divides 111 without a remainder.

1,3,37,111

Greatest Common Factor

We found the factors and prime factorization of 105 and 111. The biggest common factor number is the GCF number.
So the greatest common factor 105 and 111 is 3.

Also check out the Least Common Multiple of 105 and 111

Properties of GCF 105 and 111

(i) The GCF of 105 and 111 is associative

GCF of 105 and 111 = GCF of 111 and 105

Related Greatest Common Factor of 105

Related Greatest Common Factor of 111

Frequently Asked Questions on GCF of 105 and 111

1. What is the GCF of 105 and 111?

Answer: GCF of 105 and 111 is 3.

2. 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.

3. What are the Factors of 111?

Answer: Factors of 111 are 1, 3, 37, 111. There are 4 integers that are factors of 111. The greatest factor of 111 is 111.

4. How to Find the GCF of 105 and 111?

Answer:

Greatest Common Factor of 105 and 111 = 3

Step 1: Find the prime factorization of 105

105 = 3 x 5 x 7

Step 2: Find the prime factorization of 111

111 = 3 x 37

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 105 and 111 is 3