What is the Greatest Common Factor of 83100 and 83109?

Greatest common factor (GCF) of 83100 and 83109 is 3.

GCF(83100,83109) = 3

We will now calculate the prime factors of 83100 and 83109, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 83100 and 83109.

How to find the GCF of 83100 and 83109?

We will first find the prime factorization of 83100 and 83109. After we will calculate the factors of 83100 and 83109 and find the biggest common factor number .

Step-1: Prime Factorization of 83100

Prime factors of 83100 are 2, 3, 5, 277. Prime factorization of 83100 in exponential form is:

83100 = 2² × 3¹ × 5² × 277¹

Step-2: Prime Factorization of 83109

Prime factors of 83109 are 3, 13, 2131. Prime factorization of 83109 in exponential form is:

83109 = 3¹ × 13¹ × 2131¹

Step-3: Factors of 83100

List of positive integer factors of 83100 that divides 83100 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 277, 300, 554, 831, 1108, 1385, 1662, 2770, 3324, 4155, 5540, 6925, 8310, 13850, 16620, 20775, 27700, 41550

Step-4: Factors of 83109

List of positive integer factors of 83109 that divides 83100 without a remainder.

1, 3, 13, 39, 2131, 6393, 27703

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 83100 and 83109. The biggest common factor number is the GCF number.
So the greatest common factor 83100 and 83109 is 3.

Also check out the Least Common Multiple of 83100 and 83109