What is the Greatest Common Factor of 31490 and 31500?

Greatest common factor (GCF) of 31490 and 31500 is 10.

GCF(31490,31500) = 10

We will now calculate the prime factors of 31490 and 31500, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31490 and 31500.

How to find the GCF of 31490 and 31500?

We will first find the prime factorization of 31490 and 31500. After we will calculate the factors of 31490 and 31500 and find the biggest common factor number .

Step-1: Prime Factorization of 31490

Prime factors of 31490 are 2, 5, 47, 67. Prime factorization of 31490 in exponential form is:

31490 = 2¹ × 5¹ × 47¹ × 67¹

Step-2: 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-3: Factors of 31490

List of positive integer factors of 31490 that divides 31490 without a remainder.

1, 2, 5, 10, 47, 67, 94, 134, 235, 335, 470, 670, 3149, 6298, 15745

Step-4: Factors of 31500

List of positive integer factors of 31500 that divides 31490 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31490 and 31500. The biggest common factor number is the GCF number.
So the greatest common factor 31490 and 31500 is 10.

Also check out the Least Common Multiple of 31490 and 31500