What is the Greatest Common Factor of 870 and 875?

Greatest common factor (GCF) of 870 and 875 is 5.

GCF(870,875) = 5

We will now calculate the prime factors of 870 and 875, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 870 and 875.

How to find the GCF of 870 and 875?

We will first find the prime factorization of 870 and 875. After we will calculate the factors of 870 and 875 and find the biggest common factor number .

Step-1: Prime Factorization of 870

Prime factors of 870 are 2, 3, 5, 29. Prime factorization of 870 in exponential form is:

870 = 2¹ × 3¹ × 5¹ × 29¹

Step-2: Prime Factorization of 875

Prime factors of 875 are 5, 7. Prime factorization of 875 in exponential form is:

875 = 5³ × 7¹

Step-3: Factors of 870

List of positive integer factors of 870 that divides 870 without a remainder.

1, 2, 3, 5, 6, 10, 15, 29, 30, 58, 87, 145, 174, 290, 435

Step-4: Factors of 875

List of positive integer factors of 875 that divides 870 without a remainder.

1, 5, 7, 25, 35, 125, 175

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 870 and 875. The biggest common factor number is the GCF number.
So the greatest common factor 870 and 875 is 5.

Also check out the Least Common Multiple of 870 and 875