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, 65 i.e. 5 largest integer by which both the numbers can be divided.
Greatest common factor (GCF) of 45 and 65 is 5.
GCF(45,65) = 5
Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;
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 65
5 | 65 |
13 | 13 |
1 |
Prime factors of 65 are 5,13. Prime factorization of 65 in exponential form is:
65 = 51×131
∴ So by taking common prime factors GCF of 45 and 65 is 5
Factors of 45
List of positive integer factors of 45 that divides 45 without a remainder.
1,3,5,9,15,45
Factors of 65
List of positive integer factors of 65 that divides 65 without a remainder.
1,5,13,65
Greatest Common Factor
We found the factors and prime factorization of 45 and 65. The biggest common factor number is the GCF number.
So the greatest common factor 45 and 65 is 5.
Also check out the Least Common Multiple of 45 and 65
(i) The GCF of 45 and 65 is associative
GCF of 45 and 65 = GCF of 65 and 45
1. What is the GCF of 45 and 65?
Answer: GCF of 45 and 65 is 5.
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 65?
Answer: Factors of 65 are 1, 5, 13, 65. There are 4 integers that are factors of 65. The greatest factor of 65 is 65.
4. How to Find the GCF of 45 and 65?
Answer:
Greatest Common Factor of 45 and 65 = 5
Step 1: Find the prime factorization of 45
45 = 3 x 3 x 5
Step 2: Find the prime factorization of 65
65 = 5 x 13
Step 3: Multiply those factors both numbers have in common in steps i) or ii) above to find the gcf:
GCF = 5
Step 4: Therefore, the greatest common factor of 45 and 65 is 5