What is the Greatest Common Factor of 4100 and 4109?

Greatest common factor (GCF) of 4100 and 4109 is 1.

GCF(4100,4109) = 1

We will now calculate the prime factors of 4100 and 4109, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 4100 and 4109.

How to find the GCF of 4100 and 4109?

We will first find the prime factorization of 4100 and 4109. After we will calculate the factors of 4100 and 4109 and find the biggest common factor number .

Step-1: Prime Factorization of 4100

Prime factors of 4100 are 2, 5, 41. Prime factorization of 4100 in exponential form is:

4100 = 2² × 5² × 41¹

Step-2: Prime Factorization of 4109

Prime factors of 4109 are 7, 587. Prime factorization of 4109 in exponential form is:

4109 = 7¹ × 587¹

Step-3: Factors of 4100

List of positive integer factors of 4100 that divides 4100 without a remainder.

1, 2, 4, 5, 10, 20, 25, 41, 50, 82, 100, 164, 205, 410, 820, 1025, 2050

Step-4: Factors of 4109

List of positive integer factors of 4109 that divides 4100 without a remainder.

1, 7, 587

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 4100 and 4109. The biggest common factor number is the GCF number.
So the greatest common factor 4100 and 4109 is 1.

Also check out the Least Common Multiple of 4100 and 4109