Greatest Common Factor of 45 and 48

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

Greatest common factor (GCF) of 45 and 48 is 3.

GCF(45,48) = 3

GCF of 45 and 48

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

GCF of:
and

Greatest Common Factor of 45 and 48

GCF of 45 and 48 is 3

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 48


2 48
2 24
2 12
2 6
3 3
1

Prime factors of 48 are 2,3. Prime factorization of 48 in exponential form is:

48 = 24×31

∴ So by taking common prime factors GCF of 45 and 48 is 3

Greatest Common Factor of 45 and 48 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 48

List of positive integer factors of 48 that divides 48 without a remainder.

1,2,3,4,6,8,12,16,24,48

Greatest Common Factor

We found the factors and prime factorization of 45 and 48. The biggest common factor number is the GCF number.
So the greatest common factor 45 and 48 is 3.

Also check out the Least Common Multiple of 45 and 48

Properties of GCF 45 and 48

(i) The GCF of 45 and 48 is associative

GCF of 45 and 48 = GCF of 48 and 45

Related Greatest Common Factor of 45

Related Greatest Common Factor of 48

Frequently Asked Questions on GCF of 45 and 48

1. What is the GCF of 45 and 48?

Answer: GCF of 45 and 48 is 3.

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 48?

Answer: Factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. There are 10 integers that are factors of 48. The greatest factor of 48 is 48.

4. How to Find the GCF of 45 and 48?

Answer:

Greatest Common Factor of 45 and 48 = 3

Step 1: Find the prime factorization of 45

45 = 3 x 3 x 5

Step 2: Find the prime factorization of 48

48 = 2 x 2 x 2 x 2 x 3

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 45 and 48 is 3