What is the Greatest Common Factor of 20085 and 20100?

Greatest common factor (GCF) of 20085 and 20100 is 15.

GCF(20085,20100) = 15

We will now calculate the prime factors of 20085 and 20100, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 20085 and 20100.

How to find the GCF of 20085 and 20100?

We will first find the prime factorization of 20085 and 20100. After we will calculate the factors of 20085 and 20100 and find the biggest common factor number .

Step-1: Prime Factorization of 20085

Prime factors of 20085 are 3, 5, 13, 103. Prime factorization of 20085 in exponential form is:

20085 = 3¹ × 5¹ × 13¹ × 103¹

Step-2: Prime Factorization of 20100

Prime factors of 20100 are 2, 3, 5, 67. Prime factorization of 20100 in exponential form is:

20100 = 2² × 3¹ × 5² × 67¹

Step-3: Factors of 20085

List of positive integer factors of 20085 that divides 20085 without a remainder.

1, 3, 5, 13, 15, 39, 65, 103, 195, 309, 515, 1339, 1545, 4017, 6695

Step-4: Factors of 20100

List of positive integer factors of 20100 that divides 20085 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 67, 75, 100, 134, 150, 201, 268, 300, 335, 402, 670, 804, 1005, 1340, 1675, 2010, 3350, 4020, 5025, 6700, 10050

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 20085 and 20100. The biggest common factor number is the GCF number.
So the greatest common factor 20085 and 20100 is 15.

Also check out the Least Common Multiple of 20085 and 20100