What is the Greatest Common Factor of 78300 and 78314?

Greatest common factor (GCF) of 78300 and 78314 is 2.

GCF(78300,78314) = 2

We will now calculate the prime factors of 78300 and 78314, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 78300 and 78314.

How to find the GCF of 78300 and 78314?

We will first find the prime factorization of 78300 and 78314. After we will calculate the factors of 78300 and 78314 and find the biggest common factor number .

Step-1: Prime Factorization of 78300

Prime factors of 78300 are 2, 3, 5, 29. Prime factorization of 78300 in exponential form is:

78300 = 2² × 3³ × 5² × 29¹

Step-2: Prime Factorization of 78314

Prime factors of 78314 are 2, 39157. Prime factorization of 78314 in exponential form is:

78314 = 2¹ × 39157¹

Step-3: Factors of 78300

List of positive integer factors of 78300 that divides 78300 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 27, 29, 30, 36, 45, 50, 54, 58, 60, 75, 87, 90, 100, 108, 116, 135, 145, 150, 174, 180, 225, 261, 270, 290, 300, 348, 435, 450, 522, 540, 580, 675, 725, 783, 870, 900, 1044, 1305, 1350, 1450, 1566, 1740, 2175, 2610, 2700, 2900, 3132, 3915, 4350, 5220, 6525, 7830, 8700, 13050, 15660, 19575, 26100, 39150

Step-4: Factors of 78314

List of positive integer factors of 78314 that divides 78300 without a remainder.

1, 2, 39157

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 78300 and 78314. The biggest common factor number is the GCF number.
So the greatest common factor 78300 and 78314 is 2.

Also check out the Least Common Multiple of 78300 and 78314