Greatest Common Factor of 60 and 63

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 60, 63 i.e. 3 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 60 and 63 is 3.

GCF(60,63) = 3

GCF of 60 and 63

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

GCF of:
and

Greatest Common Factor of 60 and 63

GCF of 60 and 63 is 3

Prime Factorization of 60


2 60
2 30
3 15
5 5
1

Prime factors of 60 are 2,3,5. Prime factorization of 60 in exponential form is:

60 = 22×31×51

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

∴ So by taking common prime factors GCF of 60 and 63 is 3

Greatest Common Factor of 60 and 63 by matching factors method

Factors of 60

List of positive integer factors of 60 that divides 60 without a remainder.

1,2,3,4,5,6,10,12,15,20,30,60

Factors of 63

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

1,3,7,9,21,63

Greatest Common Factor

We found the factors and prime factorization of 60 and 63. The biggest common factor number is the GCF number.
So the greatest common factor 60 and 63 is 3.

Also check out the Least Common Multiple of 60 and 63

Properties of GCF 60 and 63

(i) The GCF of 60 and 63 is associative

GCF of 60 and 63 = GCF of 63 and 60

Related Greatest Common Factor of 60

Related Greatest Common Factor of 63

Frequently Asked Questions on GCF of 60 and 63

1. What is the GCF of 60 and 63?

Answer: GCF of 60 and 63 is 3.

2. What are the Factors of 60?

Answer: Factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60. There are 12 integers that are factors of 60. The greatest factor of 60 is 60.

3. 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.

4. How to Find the GCF of 60 and 63?

Answer:

Greatest Common Factor of 60 and 63 = 3

Step 1: Find the prime factorization of 60

60 = 2 x 2 x 3 x 5

Step 2: Find the prime factorization of 63

63 = 3 x 3 x 7

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 60 and 63 is 3