What is the Greatest Common Factor of 31125 and 31140?

Greatest common factor (GCF) of 31125 and 31140 is 15.

GCF(31125,31140) = 15

We will now calculate the prime factors of 31125 and 31140, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31125 and 31140.

How to find the GCF of 31125 and 31140?

We will first find the prime factorization of 31125 and 31140. After we will calculate the factors of 31125 and 31140 and find the biggest common factor number .

Step-1: Prime Factorization of 31125

Prime factors of 31125 are 3, 5, 83. Prime factorization of 31125 in exponential form is:

31125 = 3¹ × 5³ × 83¹

Step-2: Prime Factorization of 31140

Prime factors of 31140 are 2, 3, 5, 173. Prime factorization of 31140 in exponential form is:

31140 = 2² × 3² × 5¹ × 173¹

Step-3: Factors of 31125

List of positive integer factors of 31125 that divides 31125 without a remainder.

1, 3, 5, 15, 25, 75, 83, 125, 249, 375, 415, 1245, 2075, 6225, 10375

Step-4: Factors of 31140

List of positive integer factors of 31140 that divides 31125 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 173, 180, 346, 519, 692, 865, 1038, 1557, 1730, 2076, 2595, 3114, 3460, 5190, 6228, 7785, 10380, 15570

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31125 and 31140. The biggest common factor number is the GCF number.
So the greatest common factor 31125 and 31140 is 15.

Also check out the Least Common Multiple of 31125 and 31140