What is the Greatest Common Factor of 82500 and 82512?

Greatest common factor (GCF) of 82500 and 82512 is 12.

GCF(82500,82512) = 12

We will now calculate the prime factors of 82500 and 82512, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 82500 and 82512.

How to find the GCF of 82500 and 82512?

We will first find the prime factorization of 82500 and 82512. After we will calculate the factors of 82500 and 82512 and find the biggest common factor number .

Step-1: Prime Factorization of 82500

Prime factors of 82500 are 2, 3, 5, 11. Prime factorization of 82500 in exponential form is:

82500 = 2² × 3¹ × 5⁴ × 11¹

Step-2: Prime Factorization of 82512

Prime factors of 82512 are 2, 3, 191. Prime factorization of 82512 in exponential form is:

82512 = 2⁴ × 3³ × 191¹

Step-3: Factors of 82500

List of positive integer factors of 82500 that divides 82500 without a remainder.

1, 2, 3, 4, 5, 6, 10, 11, 12, 15, 20, 22, 25, 30, 33, 44, 50, 55, 60, 66, 75, 100, 110, 125, 132, 150, 165, 220, 250, 275, 300, 330, 375, 500, 550, 625, 660, 750, 825, 1100, 1250, 1375, 1500, 1650, 1875, 2500, 2750, 3300, 3750, 4125, 5500, 6875, 7500, 8250, 13750, 16500, 20625, 27500, 41250

Step-4: Factors of 82512

List of positive integer factors of 82512 that divides 82500 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 108, 144, 191, 216, 382, 432, 573, 764, 1146, 1528, 1719, 2292, 3056, 3438, 4584, 5157, 6876, 9168, 10314, 13752, 20628, 27504, 41256

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 82500 and 82512. The biggest common factor number is the GCF number.
So the greatest common factor 82500 and 82512 is 12.

Also check out the Least Common Multiple of 82500 and 82512