What is the Greatest Common Factor of 31275 and 31280?

Greatest common factor (GCF) of 31275 and 31280 is 5.

GCF(31275,31280) = 5

We will now calculate the prime factors of 31275 and 31280, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31275 and 31280.

How to find the GCF of 31275 and 31280?

We will first find the prime factorization of 31275 and 31280. After we will calculate the factors of 31275 and 31280 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 31280

Prime factors of 31280 are 2, 5, 17, 23. Prime factorization of 31280 in exponential form is:

31280 = 2⁴ × 5¹ × 17¹ × 23¹

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 31280

List of positive integer factors of 31280 that divides 31275 without a remainder.

1, 2, 4, 5, 8, 10, 16, 17, 20, 23, 34, 40, 46, 68, 80, 85, 92, 115, 136, 170, 184, 230, 272, 340, 368, 391, 460, 680, 782, 920, 1360, 1564, 1840, 1955, 3128, 3910, 6256, 7820, 15640

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31275 and 31280. The biggest common factor number is the GCF number.
So the greatest common factor 31275 and 31280 is 5.

Also check out the Least Common Multiple of 31275 and 31280