What is the Greatest Common Factor of 31270 and 31290?

Greatest common factor (GCF) of 31270 and 31290 is 10.

GCF(31270,31290) = 10

We will now calculate the prime factors of 31270 and 31290, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31270 and 31290.

How to find the GCF of 31270 and 31290?

We will first find the prime factorization of 31270 and 31290. After we will calculate the factors of 31270 and 31290 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 31290

Prime factors of 31290 are 2, 3, 5, 7, 149. Prime factorization of 31290 in exponential form is:

31290 = 2¹ × 3¹ × 5¹ × 7¹ × 149¹

Step-3: Factors of 31270

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

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

Step-4: Factors of 31290

List of positive integer factors of 31290 that divides 31270 without a remainder.

1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 149, 210, 298, 447, 745, 894, 1043, 1490, 2086, 2235, 3129, 4470, 5215, 6258, 10430, 15645

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31270 and 31290. The biggest common factor number is the GCF number.
So the greatest common factor 31270 and 31290 is 10.

Also check out the Least Common Multiple of 31270 and 31290