What is the Greatest Common Factor of 64400 and 64414?

Greatest common factor (GCF) of 64400 and 64414 is 14.

GCF(64400,64414) = 14

We will now calculate the prime factors of 64400 and 64414, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 64400 and 64414.

How to find the GCF of 64400 and 64414?

We will first find the prime factorization of 64400 and 64414. After we will calculate the factors of 64400 and 64414 and find the biggest common factor number .

Step-1: Prime Factorization of 64400

Prime factors of 64400 are 2, 5, 7, 23. Prime factorization of 64400 in exponential form is:

64400 = 2⁴ × 5² × 7¹ × 23¹

Step-2: Prime Factorization of 64414

Prime factors of 64414 are 2, 7, 43, 107. Prime factorization of 64414 in exponential form is:

64414 = 2¹ × 7¹ × 43¹ × 107¹

Step-3: Factors of 64400

List of positive integer factors of 64400 that divides 64400 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 23, 25, 28, 35, 40, 46, 50, 56, 70, 80, 92, 100, 112, 115, 140, 161, 175, 184, 200, 230, 280, 322, 350, 368, 400, 460, 560, 575, 644, 700, 805, 920, 1150, 1288, 1400, 1610, 1840, 2300, 2576, 2800, 3220, 4025, 4600, 6440, 8050, 9200, 12880, 16100, 32200

Step-4: Factors of 64414

List of positive integer factors of 64414 that divides 64400 without a remainder.

1, 2, 7, 14, 43, 86, 107, 214, 301, 602, 749, 1498, 4601, 9202, 32207

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 64400 and 64414. The biggest common factor number is the GCF number.
So the greatest common factor 64400 and 64414 is 14.

Also check out the Least Common Multiple of 64400 and 64414