What is the Greatest Common Factor of 31425 and 31440?

Greatest common factor (GCF) of 31425 and 31440 is 15.

GCF(31425,31440) = 15

We will now calculate the prime factors of 31425 and 31440, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31425 and 31440.

How to find the GCF of 31425 and 31440?

We will first find the prime factorization of 31425 and 31440. After we will calculate the factors of 31425 and 31440 and find the biggest common factor number .

Step-1: Prime Factorization of 31425

Prime factors of 31425 are 3, 5, 419. Prime factorization of 31425 in exponential form is:

31425 = 3¹ × 5² × 419¹

Step-2: Prime Factorization of 31440

Prime factors of 31440 are 2, 3, 5, 131. Prime factorization of 31440 in exponential form is:

31440 = 2⁴ × 3¹ × 5¹ × 131¹

Step-3: Factors of 31425

List of positive integer factors of 31425 that divides 31425 without a remainder.

1, 3, 5, 15, 25, 75, 419, 1257, 2095, 6285, 10475

Step-4: Factors of 31440

List of positive integer factors of 31440 that divides 31425 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 131, 240, 262, 393, 524, 655, 786, 1048, 1310, 1572, 1965, 2096, 2620, 3144, 3930, 5240, 6288, 7860, 10480, 15720

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31425 and 31440. The biggest common factor number is the GCF number.
So the greatest common factor 31425 and 31440 is 15.

Also check out the Least Common Multiple of 31425 and 31440