# Greatest Common Factor of 30 and 45

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 30, 45 i.e. 15 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 30 and 45 is 15.

GCF(30,45) = 15

## GCF of 30 and 45

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

GCF of:
and ### GCF of 30 and 45 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 30

 2 30 3 15 5 5 1

Prime factors of 30 are 2,3,5. Prime factorization of 30 in exponential form is:

30 = 21×31×51

∴ So by taking common prime factors GCF of 45 and 30 is 15

### Greatest Common Factor of 45 and 30 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 30

List of positive integer factors of 30 that divides 30 without a remainder.

1,2,3,5,6,10,15,30

Greatest Common Factor

We found the factors and prime factorization of 45 and 30. The biggest common factor number is the GCF number.
So the greatest common factor 45 and 30 is 15.

Also check out the Least Common Multiple of 45 and 30

### Properties of GCF 45 and 30

(i) The GCF of 45 and 30 is associative

GCF of 45 and 30 = GCF of 30 and 45

### Frequently Asked Questions on GCF of 45 and 30

1. What is the GCF of 45 and 30?

Answer: GCF of 45 and 30 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 30?

Answer: Factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30. There are 8 integers that are factors of 30. The greatest factor of 30 is 30.

4. How to Find the GCF of 45 and 30?

Greatest Common Factor of 45 and 30 = 15

Step 1: Find the prime factorization of 45

45 = 3 x 3 x 5

Step 2: Find the prime factorization of 30

30 = 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 30 is 15