What is the Greatest Common Factor of 10082 and 10100?

Greatest common factor (GCF) of 10082 and 10100 is 2.

GCF(10082,10100) = 2

We will now calculate the prime factors of 10082 and 10100, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10082 and 10100.

How to find the GCF of 10082 and 10100?

We will first find the prime factorization of 10082 and 10100. After we will calculate the factors of 10082 and 10100 and find the biggest common factor number .

Step-1: Prime Factorization of 10082

Prime factors of 10082 are 2, 71. Prime factorization of 10082 in exponential form is:

10082 = 2¹ × 71²

Step-2: Prime Factorization of 10100

Prime factors of 10100 are 2, 5, 101. Prime factorization of 10100 in exponential form is:

10100 = 2² × 5² × 101¹

Step-3: Factors of 10082

List of positive integer factors of 10082 that divides 10082 without a remainder.

1, 2, 71, 142, 5041

Step-4: Factors of 10100

List of positive integer factors of 10100 that divides 10082 without a remainder.

1, 2, 4, 5, 10, 20, 25, 50, 100, 101, 202, 404, 505, 1010, 2020, 2525, 5050

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10082 and 10100. The biggest common factor number is the GCF number.
So the greatest common factor 10082 and 10100 is 2.

Also check out the Least Common Multiple of 10082 and 10100