What is the Greatest Common Factor of 82509 and 82516?

Greatest common factor (GCF) of 82509 and 82516 is 7.

GCF(82509,82516) = 7

We will now calculate the prime factors of 82509 and 82516, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 82509 and 82516.

How to find the GCF of 82509 and 82516?

We will first find the prime factorization of 82509 and 82516. After we will calculate the factors of 82509 and 82516 and find the biggest common factor number .

Step-1: Prime Factorization of 82509

Prime factors of 82509 are 3, 7, 3929. Prime factorization of 82509 in exponential form is:

82509 = 3¹ × 7¹ × 3929¹

Step-2: Prime Factorization of 82516

Prime factors of 82516 are 2, 7, 421. Prime factorization of 82516 in exponential form is:

82516 = 2² × 7² × 421¹

Step-3: Factors of 82509

List of positive integer factors of 82509 that divides 82509 without a remainder.

1, 3, 7, 21, 3929, 11787, 27503

Step-4: Factors of 82516

List of positive integer factors of 82516 that divides 82509 without a remainder.

1, 2, 4, 7, 14, 28, 49, 98, 196, 421, 842, 1684, 2947, 5894, 11788, 20629, 41258

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 82509 and 82516. The biggest common factor number is the GCF number.
So the greatest common factor 82509 and 82516 is 7.

Also check out the Least Common Multiple of 82509 and 82516