What is the Greatest Common Factor of 78309 and 78320?

Greatest common factor (GCF) of 78309 and 78320 is 11.

GCF(78309,78320) = 11

We will now calculate the prime factors of 78309 and 78320, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 78309 and 78320.

How to find the GCF of 78309 and 78320?

We will first find the prime factorization of 78309 and 78320. After we will calculate the factors of 78309 and 78320 and find the biggest common factor number .

Step-1: Prime Factorization of 78309

Prime factors of 78309 are 3, 7, 11, 113. Prime factorization of 78309 in exponential form is:

78309 = 3² × 7¹ × 11¹ × 113¹

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 78309

List of positive integer factors of 78309 that divides 78309 without a remainder.

1, 3, 7, 9, 11, 21, 33, 63, 77, 99, 113, 231, 339, 693, 791, 1017, 1243, 2373, 3729, 7119, 8701, 11187, 26103

Step-4: Factors of 78320

List of positive integer factors of 78320 that divides 78309 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 78309 and 78320. The biggest common factor number is the GCF number.
So the greatest common factor 78309 and 78320 is 11.

Also check out the Least Common Multiple of 78309 and 78320