Greatest Common Factor of 270 and 272

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 270, 272 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 270 and 272 is 2.

GCF(270,272) = 2

GCF of 270 and 272

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

GCF of:
and

Greatest Common Factor of 270 and 272

GCF of 270 and 272 is 2

Prime Factorization of 270


2 270
3 135
3 45
3 15
5 5
1

Prime factors of 270 are 2,3,5. Prime factorization of 270 in exponential form is:

270 = 21×33×51

Prime Factorization of 272


2 272
2 136
2 68
2 34
17 17
1

Prime factors of 272 are 2,17. Prime factorization of 272 in exponential form is:

272 = 24×171

∴ So by taking common prime factors GCF of 270 and 272 is 2

Greatest Common Factor of 270 and 272 by matching factors method

Factors of 270

List of positive integer factors of 270 that divides 270 without a remainder.

1,2,3,5,6,9,10,15,18,27,30,45,54,90,135,270

Factors of 272

List of positive integer factors of 272 that divides 272 without a remainder.

1,2,4,8,16,17,34,68,136,272

Greatest Common Factor

We found the factors and prime factorization of 270 and 272. The biggest common factor number is the GCF number.
So the greatest common factor 270 and 272 is 2.

Also check out the Least Common Multiple of 270 and 272

Properties of GCF 270 and 272

(i) The GCF of 270 and 272 is associative

GCF of 270 and 272 = GCF of 272 and 270

Related Greatest Common Factor of 270

Related Greatest Common Factor of 272

Frequently Asked Questions on GCF of 270 and 272

1. What is the GCF of 270 and 272?

Answer: GCF of 270 and 272 is 2.

2. What are the Factors of 270?

Answer: Factors of 270 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, 270. There are 16 integers that are factors of 270. The greatest factor of 270 is 270.

3. What are the Factors of 272?

Answer: Factors of 272 are 1, 2, 4, 8, 16, 17, 34, 68, 136, 272. There are 10 integers that are factors of 272. The greatest factor of 272 is 272.

4. How to Find the GCF of 270 and 272?

Answer:

Greatest Common Factor of 270 and 272 = 2

Step 1: Find the prime factorization of 270

270 = 2 x 3 x 3 x 3 x 5

Step 2: Find the prime factorization of 272

272 = 2 x 2 x 2 x 2 x 17

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 270 and 272 is 2