Greatest Common Factor of 538 and 540

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

Greatest common factor (GCF) of 538 and 540 is 2.

GCF(538,540) = 2

GCF of 538 and 540

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

GCF of:
and

Greatest Common Factor of 538 and 540

GCF of 538 and 540 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 540


2 540
2 270
3 135
3 45
3 15
5 5
1

Prime factors of 540 are 2,3,5. Prime factorization of 540 in exponential form is:

540 = 22×33×51

∴ So by taking common prime factors GCF of 538 and 540 is 2

Greatest Common Factor of 538 and 540 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 540

List of positive integer factors of 540 that divides 540 without a remainder.

1,2,3,4,5,6,9,10,12,15,18,20,27,30,36,45,54,60,90,108,135,180,270,540

Greatest Common Factor

We found the factors and prime factorization of 538 and 540. The biggest common factor number is the GCF number.
So the greatest common factor 538 and 540 is 2.

Also check out the Least Common Multiple of 538 and 540

Properties of GCF 538 and 540

(i) The GCF of 538 and 540 is associative

GCF of 538 and 540 = GCF of 540 and 538

Related Greatest Common Factor of 538

Related Greatest Common Factor of 540

Frequently Asked Questions on GCF of 538 and 540

1. What is the GCF of 538 and 540?

Answer: GCF of 538 and 540 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 540?

Answer: Factors of 540 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 90, 108, 135, 180, 270, 540. There are 24 integers that are factors of 540. The greatest factor of 540 is 540.

4. How to Find the GCF of 538 and 540?

Answer:

Greatest Common Factor of 538 and 540 = 2

Step 1: Find the prime factorization of 538

538 = 2 x 269

Step 2: Find the prime factorization of 540

540 = 2 x 2 x 3 x 3 x 3 x 5

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 540 is 2