Greatest Common Factor of 234 and 240

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 234, 240 i.e. 6 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 234 and 240 is 6.

GCF(234,240) = 6

GCF of 234 and 240

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

GCF of:
and

Greatest Common Factor of 234 and 240

GCF of 234 and 240 is 6

Prime Factorization of 234


2 234
3 117
3 39
13 13
1

Prime factors of 234 are 2,3,13. Prime factorization of 234 in exponential form is:

234 = 21×32×131

Prime Factorization of 240


2 240
2 120
2 60
2 30
3 15
5 5
1

Prime factors of 240 are 2,3,5. Prime factorization of 240 in exponential form is:

240 = 24×31×51

∴ So by taking common prime factors GCF of 234 and 240 is 6

Greatest Common Factor of 234 and 240 by matching factors method

Factors of 234

List of positive integer factors of 234 that divides 234 without a remainder.

1,2,3,6,9,13,18,26,39,78,117,234

Factors of 240

List of positive integer factors of 240 that divides 240 without a remainder.

1,2,3,4,5,6,8,10,12,15,16,20,24,30,40,48,60,80,120,240

Greatest Common Factor

We found the factors and prime factorization of 234 and 240. The biggest common factor number is the GCF number.
So the greatest common factor 234 and 240 is 6.

Also check out the Least Common Multiple of 234 and 240

Properties of GCF 234 and 240

(i) The GCF of 234 and 240 is associative

GCF of 234 and 240 = GCF of 240 and 234

Related Greatest Common Factor of 234

Related Greatest Common Factor of 240

Frequently Asked Questions on GCF of 234 and 240

1. What is the GCF of 234 and 240?

Answer: GCF of 234 and 240 is 6.

2. What are the Factors of 234?

Answer: Factors of 234 are 1, 2, 3, 6, 9, 13, 18, 26, 39, 78, 117, 234. There are 12 integers that are factors of 234. The greatest factor of 234 is 234.

3. What are the Factors of 240?

Answer: Factors of 240 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240. There are 20 integers that are factors of 240. The greatest factor of 240 is 240.

4. How to Find the GCF of 234 and 240?

Answer:

Greatest Common Factor of 234 and 240 = 6

Step 1: Find the prime factorization of 234

234 = 2 x 3 x 3 x 13

Step 2: Find the prime factorization of 240

240 = 2 x 2 x 2 x 2 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 234 and 240 is 6