What is the Greatest Common Factor of 10100 and 10110?

Greatest common factor (GCF) of 10100 and 10110 is 10.

GCF(10100,10110) = 10

We will now calculate the prime factors of 10100 and 10110, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10100 and 10110.

How to find the GCF of 10100 and 10110?

We will first find the prime factorization of 10100 and 10110. After we will calculate the factors of 10100 and 10110 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 10110

Prime factors of 10110 are 2, 3, 5, 337. Prime factorization of 10110 in exponential form is:

10110 = 2¹ × 3¹ × 5¹ × 337¹

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 10110

List of positive integer factors of 10110 that divides 10100 without a remainder.

1, 2, 3, 5, 6, 10, 15, 30, 337, 674, 1011, 1685, 2022, 3370, 5055

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10100 and 10110. The biggest common factor number is the GCF number.
So the greatest common factor 10100 and 10110 is 10.

Also check out the Least Common Multiple of 10100 and 10110