What is the Greatest Common Factor of 870 and 880?

Greatest common factor (GCF) of 870 and 880 is 10.

GCF(870,880) = 10

We will now calculate the prime factors of 870 and 880, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 870 and 880.

How to find the GCF of 870 and 880?

We will first find the prime factorization of 870 and 880. After we will calculate the factors of 870 and 880 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 880

Prime factors of 880 are 2, 5, 11. Prime factorization of 880 in exponential form is:

880 = 2⁴ × 5¹ × 11¹

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 880

List of positive integer factors of 880 that divides 870 without a remainder.

1, 2, 4, 5, 8, 10, 11, 16, 20, 22, 40, 44, 55, 80, 88, 110, 176, 220, 440

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 870 and 880. The biggest common factor number is the GCF number.
So the greatest common factor 870 and 880 is 10.

Also check out the Least Common Multiple of 870 and 880