What is the Greatest Common Factor of 82125 and 82134?

Greatest common factor (GCF) of 82125 and 82134 is 9.

GCF(82125,82134) = 9

We will now calculate the prime factors of 82125 and 82134, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 82125 and 82134.

How to find the GCF of 82125 and 82134?

We will first find the prime factorization of 82125 and 82134. After we will calculate the factors of 82125 and 82134 and find the biggest common factor number .

Step-1: Prime Factorization of 82125

Prime factors of 82125 are 3, 5, 73. Prime factorization of 82125 in exponential form is:

82125 = 3² × 5³ × 73¹

Step-2: Prime Factorization of 82134

Prime factors of 82134 are 2, 3, 13. Prime factorization of 82134 in exponential form is:

82134 = 2¹ × 3⁵ × 13²

Step-3: Factors of 82125

List of positive integer factors of 82125 that divides 82125 without a remainder.

1, 3, 5, 9, 15, 25, 45, 73, 75, 125, 219, 225, 365, 375, 657, 1095, 1125, 1825, 3285, 5475, 9125, 16425, 27375

Step-4: Factors of 82134

List of positive integer factors of 82134 that divides 82125 without a remainder.

1, 2, 3, 6, 9, 13, 18, 26, 27, 39, 54, 78, 81, 117, 162, 169, 234, 243, 338, 351, 486, 507, 702, 1014, 1053, 1521, 2106, 3042, 3159, 4563, 6318, 9126, 13689, 27378, 41067

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 82125 and 82134. The biggest common factor number is the GCF number.
So the greatest common factor 82125 and 82134 is 9.

Also check out the Least Common Multiple of 82125 and 82134