Greatest Common Factor of 66 and 69

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, 69 i.e. 3 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 66 and 69 is 3.

GCF(66,69) = 3

GCF of 66 and 69

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

GCF of:
and

Greatest Common Factor of 66 and 69

GCF of 66 and 69 is 3

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 69


3 69
23 23
1

Prime factors of 69 are 3,23. Prime factorization of 69 in exponential form is:

69 = 31×231

∴ So by taking common prime factors GCF of 66 and 69 is 3

Greatest Common Factor of 66 and 69 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 69

List of positive integer factors of 69 that divides 69 without a remainder.

1,3,23,69

Greatest Common Factor

We found the factors and prime factorization of 66 and 69. The biggest common factor number is the GCF number.
So the greatest common factor 66 and 69 is 3.

Also check out the Least Common Multiple of 66 and 69

Properties of GCF 66 and 69

(i) The GCF of 66 and 69 is associative

GCF of 66 and 69 = GCF of 69 and 66

Related Greatest Common Factor of 66

Related Greatest Common Factor of 69

Frequently Asked Questions on GCF of 66 and 69

1. What is the GCF of 66 and 69?

Answer: GCF of 66 and 69 is 3.

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 69?

Answer: Factors of 69 are 1, 3, 23, 69. There are 4 integers that are factors of 69. The greatest factor of 69 is 69.

4. How to Find the GCF of 66 and 69?

Answer:

Greatest Common Factor of 66 and 69 = 3

Step 1: Find the prime factorization of 66

66 = 2 x 3 x 11

Step 2: Find the prime factorization of 69

69 = 3 x 23

Step 3: Multiply those factors both numbers have in common in steps i) or ii) above to find the gcf:

GCF = 3

Step 4: Therefore, the greatest common factor of 66 and 69 is 3