What is the Greatest Common Factor of 82096 and 82100?

Greatest common factor (GCF) of 82096 and 82100 is 4.

GCF(82096,82100) = 4

We will now calculate the prime factors of 82096 and 82100, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 82096 and 82100.

How to find the GCF of 82096 and 82100?

We will first find the prime factorization of 82096 and 82100. After we will calculate the factors of 82096 and 82100 and find the biggest common factor number .

Step-1: Prime Factorization of 82096

Prime factors of 82096 are 2, 7, 733. Prime factorization of 82096 in exponential form is:

82096 = 2⁴ × 7¹ × 733¹

Step-2: Prime Factorization of 82100

Prime factors of 82100 are 2, 5, 821. Prime factorization of 82100 in exponential form is:

82100 = 2² × 5² × 821¹

Step-3: Factors of 82096

List of positive integer factors of 82096 that divides 82096 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 56, 112, 733, 1466, 2932, 5131, 5864, 10262, 11728, 20524, 41048

Step-4: Factors of 82100

List of positive integer factors of 82100 that divides 82096 without a remainder.

1, 2, 4, 5, 10, 20, 25, 50, 100, 821, 1642, 3284, 4105, 8210, 16420, 20525, 41050

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 82096 and 82100. The biggest common factor number is the GCF number.
So the greatest common factor 82096 and 82100 is 4.

Also check out the Least Common Multiple of 82096 and 82100