What is the Greatest Common Factor of 82400 and 82416?

Greatest common factor (GCF) of 82400 and 82416 is 16.

GCF(82400,82416) = 16

We will now calculate the prime factors of 82400 and 82416, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 82400 and 82416.

How to find the GCF of 82400 and 82416?

We will first find the prime factorization of 82400 and 82416. After we will calculate the factors of 82400 and 82416 and find the biggest common factor number .

Step-1: Prime Factorization of 82400

Prime factors of 82400 are 2, 5, 103. Prime factorization of 82400 in exponential form is:

82400 = 2⁵ × 5² × 103¹

Step-2: Prime Factorization of 82416

Prime factors of 82416 are 2, 3, 17, 101. Prime factorization of 82416 in exponential form is:

82416 = 2⁴ × 3¹ × 17¹ × 101¹

Step-3: Factors of 82400

List of positive integer factors of 82400 that divides 82400 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 103, 160, 200, 206, 400, 412, 515, 800, 824, 1030, 1648, 2060, 2575, 3296, 4120, 5150, 8240, 10300, 16480, 20600, 41200

Step-4: Factors of 82416

List of positive integer factors of 82416 that divides 82400 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 17, 24, 34, 48, 51, 68, 101, 102, 136, 202, 204, 272, 303, 404, 408, 606, 808, 816, 1212, 1616, 1717, 2424, 3434, 4848, 5151, 6868, 10302, 13736, 20604, 27472, 41208

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 82400 and 82416. The biggest common factor number is the GCF number.
So the greatest common factor 82400 and 82416 is 16.

Also check out the Least Common Multiple of 82400 and 82416