What is the Greatest Common Factor of 10100 and 10116?

Greatest common factor (GCF) of 10100 and 10116 is 4.

GCF(10100,10116) = 4

We will now calculate the prime factors of 10100 and 10116, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10100 and 10116.

How to find the GCF of 10100 and 10116?

We will first find the prime factorization of 10100 and 10116. After we will calculate the factors of 10100 and 10116 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 10116

Prime factors of 10116 are 2, 3, 281. Prime factorization of 10116 in exponential form is:

10116 = 2² × 3² × 281¹

Step-3: Factors of 10100

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

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

Step-4: Factors of 10116

List of positive integer factors of 10116 that divides 10100 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 36, 281, 562, 843, 1124, 1686, 2529, 3372, 5058

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10100 and 10116. The biggest common factor number is the GCF number.
So the greatest common factor 10100 and 10116 is 4.

Also check out the Least Common Multiple of 10100 and 10116