Greatest Common Factor of 105 and 539

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, 539 i.e. 7 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 105 and 539 is 7.

GCF(105,539) = 7

GCF of 105 and 539

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

GCF of:
and

Greatest Common Factor of 105 and 539

GCF of 105 and 539 is 7

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 539


7 539
7 77
11 11
1

Prime factors of 539 are 7,11. Prime factorization of 539 in exponential form is:

539 = 72×111

∴ So by taking common prime factors GCF of 105 and 539 is 7

Greatest Common Factor of 105 and 539 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 539

List of positive integer factors of 539 that divides 539 without a remainder.

1,7,11,49,77,539

Greatest Common Factor

We found the factors and prime factorization of 105 and 539. The biggest common factor number is the GCF number.
So the greatest common factor 105 and 539 is 7.

Also check out the Least Common Multiple of 105 and 539

Properties of GCF 105 and 539

(i) The GCF of 105 and 539 is associative

GCF of 105 and 539 = GCF of 539 and 105

Related Greatest Common Factor of 105

Related Greatest Common Factor of 539

Frequently Asked Questions on GCF of 105 and 539

1. What is the GCF of 105 and 539?

Answer: GCF of 105 and 539 is 7.

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 539?

Answer: Factors of 539 are 1, 7, 11, 49, 77, 539. There are 6 integers that are factors of 539. The greatest factor of 539 is 539.

4. How to Find the GCF of 105 and 539?

Answer:

Greatest Common Factor of 105 and 539 = 7

Step 1: Find the prime factorization of 105

105 = 3 x 5 x 7

Step 2: Find the prime factorization of 539

539 = 7 x 7 x 11

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

GCF = 7

Step 4: Therefore, the greatest common factor of 105 and 539 is 7