What is the Greatest Common Factor of 31250 and 31270?

Greatest common factor (GCF) of 31250 and 31270 is 10.

GCF(31250,31270) = 10

We will now calculate the prime factors of 31250 and 31270, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31250 and 31270.

How to find the GCF of 31250 and 31270?

We will first find the prime factorization of 31250 and 31270. After we will calculate the factors of 31250 and 31270 and find the biggest common factor number .

Step-1: Prime Factorization of 31250

Prime factors of 31250 are 2, 5. Prime factorization of 31250 in exponential form is:

31250 = 2¹ × 5⁶

Step-2: Prime Factorization of 31270

Prime factors of 31270 are 2, 5, 53, 59. Prime factorization of 31270 in exponential form is:

31270 = 2¹ × 5¹ × 53¹ × 59¹

Step-3: Factors of 31250

List of positive integer factors of 31250 that divides 31250 without a remainder.

1, 2, 5, 10, 25, 50, 125, 250, 625, 1250, 3125, 6250, 15625

Step-4: Factors of 31270

List of positive integer factors of 31270 that divides 31250 without a remainder.

1, 2, 5, 10, 53, 59, 106, 118, 265, 295, 530, 590, 3127, 6254, 15635

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31250 and 31270. The biggest common factor number is the GCF number.
So the greatest common factor 31250 and 31270 is 10.

Also check out the Least Common Multiple of 31250 and 31270