Greatest Common Factor of 264 and 270

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 264, 270 i.e. 6 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 264 and 270 is 6.

GCF(264,270) = 6

GCF of 264 and 270

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

GCF of:
and

Greatest Common Factor of 264 and 270

GCF of 264 and 270 is 6

Prime Factorization of 264


2 264
2 132
2 66
3 33
11 11
1

Prime factors of 264 are 2,3,11. Prime factorization of 264 in exponential form is:

264 = 23×31×111

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

∴ So by taking common prime factors GCF of 264 and 270 is 6

Greatest Common Factor of 264 and 270 by matching factors method

Factors of 264

List of positive integer factors of 264 that divides 264 without a remainder.

1,2,3,4,6,8,11,12,22,24,33,44,66,88,132,264

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

Greatest Common Factor

We found the factors and prime factorization of 264 and 270. The biggest common factor number is the GCF number.
So the greatest common factor 264 and 270 is 6.

Also check out the Least Common Multiple of 264 and 270

Properties of GCF 264 and 270

(i) The GCF of 264 and 270 is associative

GCF of 264 and 270 = GCF of 270 and 264

Related Greatest Common Factor of 264

Related Greatest Common Factor of 270

Frequently Asked Questions on GCF of 264 and 270

1. What is the GCF of 264 and 270?

Answer: GCF of 264 and 270 is 6.

2. What are the Factors of 264?

Answer: Factors of 264 are 1, 2, 3, 4, 6, 8, 11, 12, 22, 24, 33, 44, 66, 88, 132, 264. There are 16 integers that are factors of 264. The greatest factor of 264 is 264.

3. 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.

4. How to Find the GCF of 264 and 270?

Answer:

Greatest Common Factor of 264 and 270 = 6

Step 1: Find the prime factorization of 264

264 = 2 x 2 x 2 x 3 x 11

Step 2: Find the prime factorization of 270

270 = 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 x 3 = 6

Step 4: Therefore, the greatest common factor of 264 and 270 is 6