What is the Greatest Common Factor of 66400 and 66414?

Greatest common factor (GCF) of 66400 and 66414 is 2.

GCF(66400,66414) = 2

We will now calculate the prime factors of 66400 and 66414, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 66400 and 66414.

How to find the GCF of 66400 and 66414?

We will first find the prime factorization of 66400 and 66414. After we will calculate the factors of 66400 and 66414 and find the biggest common factor number .

Step-1: Prime Factorization of 66400

Prime factors of 66400 are 2, 5, 83. Prime factorization of 66400 in exponential form is:

66400 = 2⁵ × 5² × 83¹

Step-2: Prime Factorization of 66414

Prime factors of 66414 are 2, 3, 11069. Prime factorization of 66414 in exponential form is:

66414 = 2¹ × 3¹ × 11069¹

Step-3: Factors of 66400

List of positive integer factors of 66400 that divides 66400 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 83, 100, 160, 166, 200, 332, 400, 415, 664, 800, 830, 1328, 1660, 2075, 2656, 3320, 4150, 6640, 8300, 13280, 16600, 33200

Step-4: Factors of 66414

List of positive integer factors of 66414 that divides 66400 without a remainder.

1, 2, 3, 6, 11069, 22138, 33207

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 66400 and 66414. The biggest common factor number is the GCF number.
So the greatest common factor 66400 and 66414 is 2.

Also check out the Least Common Multiple of 66400 and 66414