What is the Greatest Common Factor of 31275 and 31290?

Greatest common factor (GCF) of 31275 and 31290 is 15.

GCF(31275,31290) = 15

We will now calculate the prime factors of 31275 and 31290, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31275 and 31290.

How to find the GCF of 31275 and 31290?

We will first find the prime factorization of 31275 and 31290. After we will calculate the factors of 31275 and 31290 and find the biggest common factor number .

Step-1: Prime Factorization of 31275

Prime factors of 31275 are 3, 5, 139. Prime factorization of 31275 in exponential form is:

31275 = 3² × 5² × 139¹

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 31275

List of positive integer factors of 31275 that divides 31275 without a remainder.

1, 3, 5, 9, 15, 25, 45, 75, 139, 225, 417, 695, 1251, 2085, 3475, 6255, 10425

Step-4: Factors of 31290

List of positive integer factors of 31290 that divides 31275 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 31275 and 31290. The biggest common factor number is the GCF number.
So the greatest common factor 31275 and 31290 is 15.

Also check out the Least Common Multiple of 31275 and 31290