Greatest Common Factor of 45 and 51

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

Greatest common factor (GCF) of 45 and 51 is 3.

GCF(45,51) = 3

GCF of 45 and 51

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

GCF of:
and

Greatest Common Factor of 45 and 51

GCF of 45 and 51 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 51


3 51
17 17
1

Prime factors of 51 are 3,17. Prime factorization of 51 in exponential form is:

51 = 31×171

∴ So by taking common prime factors GCF of 45 and 51 is 3

Greatest Common Factor of 45 and 51 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 51

List of positive integer factors of 51 that divides 51 without a remainder.

1,3,17,51

Greatest Common Factor

We found the factors and prime factorization of 45 and 51. The biggest common factor number is the GCF number.
So the greatest common factor 45 and 51 is 3.

Also check out the Least Common Multiple of 45 and 51

Properties of GCF 45 and 51

(i) The GCF of 45 and 51 is associative

GCF of 45 and 51 = GCF of 51 and 45

Related Greatest Common Factor of 45

Related Greatest Common Factor of 51

Frequently Asked Questions on GCF of 45 and 51

1. What is the GCF of 45 and 51?

Answer: GCF of 45 and 51 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 51?

Answer: Factors of 51 are 1, 3, 17, 51. There are 4 integers that are factors of 51. The greatest factor of 51 is 51.

4. How to Find the GCF of 45 and 51?

Answer:

Greatest Common Factor of 45 and 51 = 3

Step 1: Find the prime factorization of 45

45 = 3 x 3 x 5

Step 2: Find the prime factorization of 51

51 = 3 x 17

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 51 is 3