What is the Greatest Common Factor of 78480 and 78500?

Greatest common factor (GCF) of 78480 and 78500 is 20.

GCF(78480,78500) = 20

We will now calculate the prime factors of 78480 and 78500, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 78480 and 78500.

How to find the GCF of 78480 and 78500?

We will first find the prime factorization of 78480 and 78500. After we will calculate the factors of 78480 and 78500 and find the biggest common factor number .

Step-1: Prime Factorization of 78480

Prime factors of 78480 are 2, 3, 5, 109. Prime factorization of 78480 in exponential form is:

78480 = 2⁴ × 3² × 5¹ × 109¹

Step-2: Prime Factorization of 78500

Prime factors of 78500 are 2, 5, 157. Prime factorization of 78500 in exponential form is:

78500 = 2² × 5³ × 157¹

Step-3: Factors of 78480

List of positive integer factors of 78480 that divides 78480 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 48, 60, 72, 80, 90, 109, 120, 144, 180, 218, 240, 327, 360, 436, 545, 654, 720, 872, 981, 1090, 1308, 1635, 1744, 1962, 2180, 2616, 3270, 3924, 4360, 4905, 5232, 6540, 7848, 8720, 9810, 13080, 15696, 19620, 26160, 39240

Step-4: Factors of 78500

List of positive integer factors of 78500 that divides 78480 without a remainder.

1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 157, 250, 314, 500, 628, 785, 1570, 3140, 3925, 7850, 15700, 19625, 39250

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 78480 and 78500. The biggest common factor number is the GCF number.
So the greatest common factor 78480 and 78500 is 20.

Also check out the Least Common Multiple of 78480 and 78500