What is the Greatest Common Factor of 31500 and 31504?

Greatest common factor (GCF) of 31500 and 31504 is 4.

GCF(31500,31504) = 4

We will now calculate the prime factors of 31500 and 31504, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31500 and 31504.

How to find the GCF of 31500 and 31504?

We will first find the prime factorization of 31500 and 31504. After we will calculate the factors of 31500 and 31504 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 31504

Prime factors of 31504 are 2, 11, 179. Prime factorization of 31504 in exponential form is:

31504 = 2⁴ × 11¹ × 179¹

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 31504

List of positive integer factors of 31504 that divides 31500 without a remainder.

1, 2, 4, 8, 11, 16, 22, 44, 88, 176, 179, 358, 716, 1432, 1969, 2864, 3938, 7876, 15752

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31500 and 31504. The biggest common factor number is the GCF number.
So the greatest common factor 31500 and 31504 is 4.

Also check out the Least Common Multiple of 31500 and 31504