What is the Greatest Common Factor of 10100 and 10120?

Greatest common factor (GCF) of 10100 and 10120 is 20.

GCF(10100,10120) = 20

We will now calculate the prime factors of 10100 and 10120, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10100 and 10120.

How to find the GCF of 10100 and 10120?

We will first find the prime factorization of 10100 and 10120. After we will calculate the factors of 10100 and 10120 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 10120

Prime factors of 10120 are 2, 5, 11, 23. Prime factorization of 10120 in exponential form is:

10120 = 2³ × 5¹ × 11¹ × 23¹

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 10120

List of positive integer factors of 10120 that divides 10100 without a remainder.

1, 2, 4, 5, 8, 10, 11, 20, 22, 23, 40, 44, 46, 55, 88, 92, 110, 115, 184, 220, 230, 253, 440, 460, 506, 920, 1012, 1265, 2024, 2530, 5060

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10100 and 10120. The biggest common factor number is the GCF number.
So the greatest common factor 10100 and 10120 is 20.

Also check out the Least Common Multiple of 10100 and 10120