Greatest Common Factor of 63 and 66

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 63, 66 i.e. 3 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 63 and 66 is 3.

GCF(63,66) = 3

GCF of 63 and 66

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

GCF of:
and

Greatest Common Factor of 63 and 66

GCF of 63 and 66 is 3

Prime Factorization of 63


3 63
3 21
7 7
1

Prime factors of 63 are 3,7. Prime factorization of 63 in exponential form is:

63 = 32×71

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

∴ So by taking common prime factors GCF of 63 and 66 is 3

Greatest Common Factor of 63 and 66 by matching factors method

Factors of 63

List of positive integer factors of 63 that divides 63 without a remainder.

1,3,7,9,21,63

Factors of 66

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

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

Greatest Common Factor

We found the factors and prime factorization of 63 and 66. The biggest common factor number is the GCF number.
So the greatest common factor 63 and 66 is 3.

Also check out the Least Common Multiple of 63 and 66

Properties of GCF 63 and 66

(i) The GCF of 63 and 66 is associative

GCF of 63 and 66 = GCF of 66 and 63

Related Greatest Common Factor of 63

Related Greatest Common Factor of 66

Frequently Asked Questions on GCF of 63 and 66

1. What is the GCF of 63 and 66?

Answer: GCF of 63 and 66 is 3.

2. What are the Factors of 63?

Answer: Factors of 63 are 1, 3, 7, 9, 21, 63. There are 6 integers that are factors of 63. The greatest factor of 63 is 63.

3. 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.

4. How to Find the GCF of 63 and 66?

Answer:

Greatest Common Factor of 63 and 66 = 3

Step 1: Find the prime factorization of 63

63 = 3 x 3 x 7

Step 2: Find the prime factorization of 66

66 = 2 x 3 x 11

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 63 and 66 is 3