What is the Greatest Common Factor of 84100 and 84114?

Greatest common factor (GCF) of 84100 and 84114 is 2.

GCF(84100,84114) = 2

We will now calculate the prime factors of 84100 and 84114, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 84100 and 84114.

How to find the GCF of 84100 and 84114?

We will first find the prime factorization of 84100 and 84114. After we will calculate the factors of 84100 and 84114 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 84114

Prime factors of 84114 are 2, 3, 4673. Prime factorization of 84114 in exponential form is:

84114 = 2¹ × 3² × 4673¹

Step-3: Factors of 84100

List of positive integer factors of 84100 that divides 84100 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

Step-4: Factors of 84114

List of positive integer factors of 84114 that divides 84100 without a remainder.

1, 2, 3, 6, 9, 18, 4673, 9346, 14019, 28038, 42057

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 84100 and 84114. The biggest common factor number is the GCF number.
So the greatest common factor 84100 and 84114 is 2.

Also check out the Least Common Multiple of 84100 and 84114