What is the Greatest Common Factor of 46400 and 46414?

Greatest common factor (GCF) of 46400 and 46414 is 2.

GCF(46400,46414) = 2

We will now calculate the prime factors of 46400 and 46414, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 46400 and 46414.

How to find the GCF of 46400 and 46414?

We will first find the prime factorization of 46400 and 46414. After we will calculate the factors of 46400 and 46414 and find the biggest common factor number .

Step-1: Prime Factorization of 46400

Prime factors of 46400 are 2, 5, 29. Prime factorization of 46400 in exponential form is:

46400 = 2⁶ × 5² × 29¹

Step-2: Prime Factorization of 46414

Prime factors of 46414 are 2, 23, 1009. Prime factorization of 46414 in exponential form is:

46414 = 2¹ × 23¹ × 1009¹

Step-3: Factors of 46400

List of positive integer factors of 46400 that divides 46400 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 29, 32, 40, 50, 58, 64, 80, 100, 116, 145, 160, 200, 232, 290, 320, 400, 464, 580, 725, 800, 928, 1160, 1450, 1600, 1856, 2320, 2900, 4640, 5800, 9280, 11600, 23200

Step-4: Factors of 46414

List of positive integer factors of 46414 that divides 46400 without a remainder.

1, 2, 23, 46, 1009, 2018, 23207

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 46400 and 46414. The biggest common factor number is the GCF number.
So the greatest common factor 46400 and 46414 is 2.

Also check out the Least Common Multiple of 46400 and 46414