What is the Greatest Common Factor of 84096 and 84100?

Greatest common factor (GCF) of 84096 and 84100 is 4.

GCF(84096,84100) = 4

We will now calculate the prime factors of 84096 and 84100, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 84096 and 84100.

How to find the GCF of 84096 and 84100?

We will first find the prime factorization of 84096 and 84100. After we will calculate the factors of 84096 and 84100 and find the biggest common factor number .

Step-1: Prime Factorization of 84096

Prime factors of 84096 are 2, 3, 73. Prime factorization of 84096 in exponential form is:

84096 = 2⁷ × 3² × 73¹

Step-2: Prime Factorization of 84100

Prime factors of 84100 are 2, 5, 29. Prime factorization of 84100 in exponential form is:

84100 = 2² × 5² × 29²

Step-3: Factors of 84096

List of positive integer factors of 84096 that divides 84096 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 73, 96, 128, 144, 146, 192, 219, 288, 292, 384, 438, 576, 584, 657, 876, 1152, 1168, 1314, 1752, 2336, 2628, 3504, 4672, 5256, 7008, 9344, 10512, 14016, 21024, 28032, 42048

Step-4: Factors of 84100

List of positive integer factors of 84100 that divides 84096 without a remainder.

1, 2, 4, 5, 10, 20, 25, 29, 50, 58, 100, 116, 145, 290, 580, 725, 841, 1450, 1682, 2900, 3364, 4205, 8410, 16820, 21025, 42050

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 84096 and 84100. The biggest common factor number is the GCF number.
So the greatest common factor 84096 and 84100 is 4.

Also check out the Least Common Multiple of 84096 and 84100