Greatest Common Factor of 160 and 175

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 160, 175 i.e. 5 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 160 and 175 is 5.

GCF(160,175) = 5

GCF of 160 and 175

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

GCF of:
and

Greatest Common Factor of 160 and 175

GCF of 160 and 175 is 5

Prime Factorization of 160


2 160
2 80
2 40
2 20
2 10
5 5
1

Prime factors of 160 are 2,5. Prime factorization of 160 in exponential form is:

160 = 25×51

Prime Factorization of 175


5 175
5 35
7 7
1

Prime factors of 175 are 5,7. Prime factorization of 175 in exponential form is:

175 = 52×71

∴ So by taking common prime factors GCF of 160 and 175 is 5

Greatest Common Factor of 160 and 175 by matching factors method

Factors of 160

List of positive integer factors of 160 that divides 160 without a remainder.

1,2,4,5,8,10,16,20,32,40,80,160

Factors of 175

List of positive integer factors of 175 that divides 175 without a remainder.

1,5,7,25,35,175

Greatest Common Factor

We found the factors and prime factorization of 160 and 175. The biggest common factor number is the GCF number.
So the greatest common factor 160 and 175 is 5.

Also check out the Least Common Multiple of 160 and 175

Properties of GCF 160 and 175

(i) The GCF of 160 and 175 is associative

GCF of 160 and 175 = GCF of 175 and 160

Related Greatest Common Factor of 160

Related Greatest Common Factor of 175

Frequently Asked Questions on GCF of 160 and 175

1. What is the GCF of 160 and 175?

Answer: GCF of 160 and 175 is 5.

2. What are the Factors of 160?

Answer: Factors of 160 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, 160. There are 12 integers that are factors of 160. The greatest factor of 160 is 160.

3. What are the Factors of 175?

Answer: Factors of 175 are 1, 5, 7, 25, 35, 175. There are 6 integers that are factors of 175. The greatest factor of 175 is 175.

4. How to Find the GCF of 160 and 175?

Answer:

Greatest Common Factor of 160 and 175 = 5

Step 1: Find the prime factorization of 160

160 = 2 x 2 x 2 x 2 x 2 x 5

Step 2: Find the prime factorization of 175

175 = 5 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 160 and 175 is 5