Greatest Common Factor of 45 and 60

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 45, 60 i.e. 15 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 45 and 60 is 15.

GCF(45,60) = 15

GCF of 45 and 60

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

GCF of:
and

Greatest Common Factor of 45 and 60

GCF of 45 and 60 is 15

Prime Factorization of 45


3 45
3 15
5 5
1

Prime factors of 45 are 3,5. Prime factorization of 45 in exponential form is:

45 = 32×51

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

∴ So by taking common prime factors GCF of 45 and 60 is 15

Greatest Common Factor of 45 and 60 by matching factors method

Factors of 45

List of positive integer factors of 45 that divides 45 without a remainder.

1,3,5,9,15,45

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

Greatest Common Factor

We found the factors and prime factorization of 45 and 60. The biggest common factor number is the GCF number.
So the greatest common factor 45 and 60 is 15.

Also check out the Least Common Multiple of 45 and 60

Properties of GCF 45 and 60

(i) The GCF of 45 and 60 is associative

GCF of 45 and 60 = GCF of 60 and 45

Related Greatest Common Factor of 45

Related Greatest Common Factor of 60

Frequently Asked Questions on GCF of 45 and 60

1. What is the GCF of 45 and 60?

Answer: GCF of 45 and 60 is 15.

2. What are the Factors of 45?

Answer: Factors of 45 are 1, 3, 5, 9, 15, 45. There are 6 integers that are factors of 45. The greatest factor of 45 is 45.

3. 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.

4. How to Find the GCF of 45 and 60?

Answer:

Greatest Common Factor of 45 and 60 = 15

Step 1: Find the prime factorization of 45

45 = 3 x 3 x 5

Step 2: Find the prime factorization of 60

60 = 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 = 3 x 5 = 15

Step 4: Therefore, the greatest common factor of 45 and 60 is 15