What is the Greatest Common Factor of 78315 and 78320?

Greatest common factor (GCF) of 78315 and 78320 is 5.

GCF(78315,78320) = 5

We will now calculate the prime factors of 78315 and 78320, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 78315 and 78320.

How to find the GCF of 78315 and 78320?

We will first find the prime factorization of 78315 and 78320. After we will calculate the factors of 78315 and 78320 and find the biggest common factor number .

Step-1: Prime Factorization of 78315

Prime factors of 78315 are 3, 5, 23, 227. Prime factorization of 78315 in exponential form is:

78315 = 3¹ × 5¹ × 23¹ × 227¹

Step-2: Prime Factorization of 78320

Prime factors of 78320 are 2, 5, 11, 89. Prime factorization of 78320 in exponential form is:

78320 = 2⁴ × 5¹ × 11¹ × 89¹

Step-3: Factors of 78315

List of positive integer factors of 78315 that divides 78315 without a remainder.

1, 3, 5, 15, 23, 69, 115, 227, 345, 681, 1135, 3405, 5221, 15663, 26105

Step-4: Factors of 78320

List of positive integer factors of 78320 that divides 78315 without a remainder.

1, 2, 4, 5, 8, 10, 11, 16, 20, 22, 40, 44, 55, 80, 88, 89, 110, 176, 178, 220, 356, 440, 445, 712, 880, 890, 979, 1424, 1780, 1958, 3560, 3916, 4895, 7120, 7832, 9790, 15664, 19580, 39160

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 78315 and 78320. The biggest common factor number is the GCF number.
So the greatest common factor 78315 and 78320 is 5.

Also check out the Least Common Multiple of 78315 and 78320