What is the Greatest Common Factor of 8084 and 8100?

Greatest common factor (GCF) of 8084 and 8100 is 4.

GCF(8084,8100) = 4

We will now calculate the prime factors of 8084 and 8100, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 8084 and 8100.

How to find the GCF of 8084 and 8100?

We will first find the prime factorization of 8084 and 8100. After we will calculate the factors of 8084 and 8100 and find the biggest common factor number .

Step-1: Prime Factorization of 8084

Prime factors of 8084 are 2, 43, 47. Prime factorization of 8084 in exponential form is:

8084 = 2² × 43¹ × 47¹

Step-2: Prime Factorization of 8100

Prime factors of 8100 are 2, 3, 5. Prime factorization of 8100 in exponential form is:

8100 = 2² × 3⁴ × 5²

Step-3: Factors of 8084

List of positive integer factors of 8084 that divides 8084 without a remainder.

1, 2, 4, 43, 47, 86, 94, 172, 188, 2021, 4042

Step-4: Factors of 8100

List of positive integer factors of 8100 that divides 8084 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 27, 30, 36, 45, 50, 54, 60, 75, 81, 90, 100, 108, 135, 150, 162, 180, 225, 270, 300, 324, 405, 450, 540, 675, 810, 900, 1350, 1620, 2025, 2700, 4050

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 8084 and 8100. The biggest common factor number is the GCF number.
So the greatest common factor 8084 and 8100 is 4.

Also check out the Least Common Multiple of 8084 and 8100