What is the Greatest Common Factor of 31500 and 31514?

Greatest common factor (GCF) of 31500 and 31514 is 14.

GCF(31500,31514) = 14

We will now calculate the prime factors of 31500 and 31514, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31500 and 31514.

How to find the GCF of 31500 and 31514?

We will first find the prime factorization of 31500 and 31514. After we will calculate the factors of 31500 and 31514 and find the biggest common factor number .

Step-1: Prime Factorization of 31500

Prime factors of 31500 are 2, 3, 5, 7. Prime factorization of 31500 in exponential form is:

31500 = 2² × 3² × 5³ × 7¹

Step-2: Prime Factorization of 31514

Prime factors of 31514 are 2, 7, 2251. Prime factorization of 31514 in exponential form is:

31514 = 2¹ × 7¹ × 2251¹

Step-3: Factors of 31500

List of positive integer factors of 31500 that divides 31500 without a remainder.

1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 25, 28, 30, 35, 36, 42, 45, 50, 60, 63, 70, 75, 84, 90, 100, 105, 125, 126, 140, 150, 175, 180, 210, 225, 250, 252, 300, 315, 350, 375, 420, 450, 500, 525, 630, 700, 750, 875, 900, 1050, 1125, 1260, 1500, 1575, 1750, 2100, 2250, 2625, 3150, 3500, 4500, 5250, 6300, 7875, 10500, 15750

Step-4: Factors of 31514

List of positive integer factors of 31514 that divides 31500 without a remainder.

1, 2, 7, 14, 2251, 4502, 15757

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31500 and 31514. The biggest common factor number is the GCF number.
So the greatest common factor 31500 and 31514 is 14.

Also check out the Least Common Multiple of 31500 and 31514