Greatest Common Factor of 365 and 370

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 365, 370 i.e. 5 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 365 and 370 is 5.

GCF(365,370) = 5

GCF of 365 and 370

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

GCF of:
and

Greatest Common Factor of 365 and 370

GCF of 365 and 370 is 5

Prime Factorization of 365


5 365
73 73
1

Prime factors of 365 are 5,73. Prime factorization of 365 in exponential form is:

365 = 51×731

Prime Factorization of 370


2 370
5 185
37 37
1

Prime factors of 370 are 2,5,37. Prime factorization of 370 in exponential form is:

370 = 21×51×371

∴ So by taking common prime factors GCF of 365 and 370 is 5

Greatest Common Factor of 365 and 370 by matching factors method

Factors of 365

List of positive integer factors of 365 that divides 365 without a remainder.

1,5,73,365

Factors of 370

List of positive integer factors of 370 that divides 370 without a remainder.

1,2,5,10,37,74,185,370

Greatest Common Factor

We found the factors and prime factorization of 365 and 370. The biggest common factor number is the GCF number.
So the greatest common factor 365 and 370 is 5.

Also check out the Least Common Multiple of 365 and 370

Properties of GCF 365 and 370

(i) The GCF of 365 and 370 is associative

GCF of 365 and 370 = GCF of 370 and 365

Related Greatest Common Factor of 365

Related Greatest Common Factor of 370

Frequently Asked Questions on GCF of 365 and 370

1. What is the GCF of 365 and 370?

Answer: GCF of 365 and 370 is 5.

2. What are the Factors of 365?

Answer: Factors of 365 are 1, 5, 73, 365. There are 4 integers that are factors of 365. The greatest factor of 365 is 365.

3. What are the Factors of 370?

Answer: Factors of 370 are 1, 2, 5, 10, 37, 74, 185, 370. There are 8 integers that are factors of 370. The greatest factor of 370 is 370.

4. How to Find the GCF of 365 and 370?

Answer:

Greatest Common Factor of 365 and 370 = 5

Step 1: Find the prime factorization of 365

365 = 5 x 73

Step 2: Find the prime factorization of 370

370 = 2 x 5 x 37

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 365 and 370 is 5