What is the Greatest Common Factor of 82500 and 82510?

Greatest common factor (GCF) of 82500 and 82510 is 10.

GCF(82500,82510) = 10

We will now calculate the prime factors of 82500 and 82510, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 82500 and 82510.

How to find the GCF of 82500 and 82510?

We will first find the prime factorization of 82500 and 82510. After we will calculate the factors of 82500 and 82510 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 82510

Prime factors of 82510 are 2, 5, 37, 223. Prime factorization of 82510 in exponential form is:

82510 = 2¹ × 5¹ × 37¹ × 223¹

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 82510

List of positive integer factors of 82510 that divides 82500 without a remainder.

1, 2, 5, 10, 37, 74, 185, 223, 370, 446, 1115, 2230, 8251, 16502, 41255

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 82500 and 82510. The biggest common factor number is the GCF number.
So the greatest common factor 82500 and 82510 is 10.

Also check out the Least Common Multiple of 82500 and 82510