What is the Greatest Common Factor of 31500 and 31507?

Greatest common factor (GCF) of 31500 and 31507 is 7.

GCF(31500,31507) = 7

We will now calculate the prime factors of 31500 and 31507, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31500 and 31507.

How to find the GCF of 31500 and 31507?

We will first find the prime factorization of 31500 and 31507. After we will calculate the factors of 31500 and 31507 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 31507

Prime factors of 31507 are 7, 643. Prime factorization of 31507 in exponential form is:

31507 = 7² × 643¹

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 31507

List of positive integer factors of 31507 that divides 31500 without a remainder.

1, 7, 49, 643, 4501

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31500 and 31507. The biggest common factor number is the GCF number.
So the greatest common factor 31500 and 31507 is 7.

Also check out the Least Common Multiple of 31500 and 31507