Greatest Common Factor of 538 and 546

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 538, 546 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 538 and 546 is 2.

GCF(538,546) = 2

GCF of 538 and 546

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

GCF of:
and

Greatest Common Factor of 538 and 546

GCF of 538 and 546 is 2

Prime Factorization of 538


2 538
269 269
1

Prime factors of 538 are 2,269. Prime factorization of 538 in exponential form is:

538 = 21×2691

Prime Factorization of 546


2 546
3 273
7 91
13 13
1

Prime factors of 546 are 2,3,7,13. Prime factorization of 546 in exponential form is:

546 = 21×31×71×131

∴ So by taking common prime factors GCF of 538 and 546 is 2

Greatest Common Factor of 538 and 546 by matching factors method

Factors of 538

List of positive integer factors of 538 that divides 538 without a remainder.

1,2,269,538

Factors of 546

List of positive integer factors of 546 that divides 546 without a remainder.

1,2,3,6,7,13,14,21,26,39,42,78,91,182,273,546

Greatest Common Factor

We found the factors and prime factorization of 538 and 546. The biggest common factor number is the GCF number.
So the greatest common factor 538 and 546 is 2.

Also check out the Least Common Multiple of 538 and 546

Properties of GCF 538 and 546

(i) The GCF of 538 and 546 is associative

GCF of 538 and 546 = GCF of 546 and 538

Related Greatest Common Factor of 538

Related Greatest Common Factor of 546

Frequently Asked Questions on GCF of 538 and 546

1. What is the GCF of 538 and 546?

Answer: GCF of 538 and 546 is 2.

2. What are the Factors of 538?

Answer: Factors of 538 are 1, 2, 269, 538. There are 4 integers that are factors of 538. The greatest factor of 538 is 538.

3. What are the Factors of 546?

Answer: Factors of 546 are 1, 2, 3, 6, 7, 13, 14, 21, 26, 39, 42, 78, 91, 182, 273, 546. There are 16 integers that are factors of 546. The greatest factor of 546 is 546.

4. How to Find the GCF of 538 and 546?

Answer:

Greatest Common Factor of 538 and 546 = 2

Step 1: Find the prime factorization of 538

538 = 2 x 269

Step 2: Find the prime factorization of 546

546 = 2 x 3 x 7 x 13

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 538 and 546 is 2