Greatest Common Factor of 66 and 68

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 66, 68 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 66 and 68 is 2.

GCF(66,68) = 2

GCF of 66 and 68

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

GCF of:
and

Greatest Common Factor of 66 and 68

GCF of 66 and 68 is 2

Prime Factorization of 66


2 66
3 33
11 11
1

Prime factors of 66 are 2,3,11. Prime factorization of 66 in exponential form is:

66 = 21×31×111

Prime Factorization of 68


2 68
2 34
17 17
1

Prime factors of 68 are 2,17. Prime factorization of 68 in exponential form is:

68 = 22×171

∴ So by taking common prime factors GCF of 66 and 68 is 2

Greatest Common Factor of 66 and 68 by matching factors method

Factors of 66

List of positive integer factors of 66 that divides 66 without a remainder.

1,2,3,6,11,22,33,66

Factors of 68

List of positive integer factors of 68 that divides 68 without a remainder.

1,2,4,17,34,68

Greatest Common Factor

We found the factors and prime factorization of 66 and 68. The biggest common factor number is the GCF number.
So the greatest common factor 66 and 68 is 2.

Also check out the Least Common Multiple of 66 and 68

Properties of GCF 66 and 68

(i) The GCF of 66 and 68 is associative

GCF of 66 and 68 = GCF of 68 and 66

Related Greatest Common Factor of 66

Related Greatest Common Factor of 68

Frequently Asked Questions on GCF of 66 and 68

1. What is the GCF of 66 and 68?

Answer: GCF of 66 and 68 is 2.

2. What are the Factors of 66?

Answer: Factors of 66 are 1, 2, 3, 6, 11, 22, 33, 66. There are 8 integers that are factors of 66. The greatest factor of 66 is 66.

3. What are the Factors of 68?

Answer: Factors of 68 are 1, 2, 4, 17, 34, 68. There are 6 integers that are factors of 68. The greatest factor of 68 is 68.

4. How to Find the GCF of 66 and 68?

Answer:

Greatest Common Factor of 66 and 68 = 2

Step 1: Find the prime factorization of 66

66 = 2 x 3 x 11

Step 2: Find the prime factorization of 68

68 = 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 66 and 68 is 2