What is the Greatest Common Factor of 10080 and 10100?

Greatest common factor (GCF) of 10080 and 10100 is 20.

GCF(10080,10100) = 20

We will now calculate the prime factors of 10080 and 10100, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10080 and 10100.

How to find the GCF of 10080 and 10100?

We will first find the prime factorization of 10080 and 10100. After we will calculate the factors of 10080 and 10100 and find the biggest common factor number .

Step-1: Prime Factorization of 10080

Prime factors of 10080 are 2, 3, 5, 7. Prime factorization of 10080 in exponential form is:

10080 = 2⁵ × 3² × 5¹ × 7¹

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 10080

List of positive integer factors of 10080 that divides 10080 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 28, 30, 32, 35, 36, 40, 42, 45, 48, 56, 60, 63, 70, 72, 80, 84, 90, 96, 105, 112, 120, 126, 140, 144, 160, 168, 180, 210, 224, 240, 252, 280, 288, 315, 336, 360, 420, 480, 504, 560, 630, 672, 720, 840, 1008, 1120, 1260, 1440, 1680, 2016, 2520, 3360, 5040

Step-4: Factors of 10100

List of positive integer factors of 10100 that divides 10080 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 10080 and 10100. The biggest common factor number is the GCF number.
So the greatest common factor 10080 and 10100 is 20.

Also check out the Least Common Multiple of 10080 and 10100