Greatest Common Factor of 65 and 70

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 65, 70 i.e. 5 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 65 and 70 is 5.

GCF(65,70) = 5

GCF of 65 and 70

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

GCF of:
and

Greatest Common Factor of 65 and 70

GCF of 65 and 70 is 5

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

Prime Factorization of 70


2 70
5 35
7 7
1

Prime factors of 70 are 2,5,7. Prime factorization of 70 in exponential form is:

70 = 21×51×71

∴ So by taking common prime factors GCF of 65 and 70 is 5

Greatest Common Factor of 65 and 70 by matching factors method

Factors of 65

List of positive integer factors of 65 that divides 65 without a remainder.

1,5,13,65

Factors of 70

List of positive integer factors of 70 that divides 70 without a remainder.

1,2,5,7,10,14,35,70

Greatest Common Factor

We found the factors and prime factorization of 65 and 70. The biggest common factor number is the GCF number.
So the greatest common factor 65 and 70 is 5.

Also check out the Least Common Multiple of 65 and 70

Properties of GCF 65 and 70

(i) The GCF of 65 and 70 is associative

GCF of 65 and 70 = GCF of 70 and 65

Related Greatest Common Factor of 65

Related Greatest Common Factor of 70

Frequently Asked Questions on GCF of 65 and 70

1. What is the GCF of 65 and 70?

Answer: GCF of 65 and 70 is 5.

2. 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.

3. What are the Factors of 70?

Answer: Factors of 70 are 1, 2, 5, 7, 10, 14, 35, 70. There are 8 integers that are factors of 70. The greatest factor of 70 is 70.

4. How to Find the GCF of 65 and 70?

Answer:

Greatest Common Factor of 65 and 70 = 5

Step 1: Find the prime factorization of 65

65 = 5 x 13

Step 2: Find the prime factorization of 70

70 = 2 x 5 x 7

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 65 and 70 is 5