What is the Greatest Common Factor of 83997 and 84009?

Greatest common factor (GCF) of 83997 and 84009 is 3.

GCF(83997,84009) = 3

We will now calculate the prime factors of 83997 and 84009, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 83997 and 84009.

How to find the GCF of 83997 and 84009?

We will first find the prime factorization of 83997 and 84009. After we will calculate the factors of 83997 and 84009 and find the biggest common factor number .

Step-1: Prime Factorization of 83997

Prime factors of 83997 are 3, 17, 61. Prime factorization of 83997 in exponential form is:

83997 = 3⁴ × 17¹ × 61¹

Step-2: Prime Factorization of 84009

Prime factors of 84009 are 3, 41, 683. Prime factorization of 84009 in exponential form is:

84009 = 3¹ × 41¹ × 683¹

Step-3: Factors of 83997

List of positive integer factors of 83997 that divides 83997 without a remainder.

1, 3, 9, 17, 27, 51, 61, 81, 153, 183, 459, 549, 1037, 1377, 1647, 3111, 4941, 9333, 27999

Step-4: Factors of 84009

List of positive integer factors of 84009 that divides 83997 without a remainder.

1, 3, 41, 123, 683, 2049, 28003

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 83997 and 84009. The biggest common factor number is the GCF number.
So the greatest common factor 83997 and 84009 is 3.

Also check out the Least Common Multiple of 83997 and 84009