What is the Greatest Common Factor of 64314 and 64320?

Greatest common factor (GCF) of 64314 and 64320 is 6.

GCF(64314,64320) = 6

We will now calculate the prime factors of 64314 and 64320, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 64314 and 64320.

How to find the GCF of 64314 and 64320?

We will first find the prime factorization of 64314 and 64320. After we will calculate the factors of 64314 and 64320 and find the biggest common factor number .

Step-1: Prime Factorization of 64314

Prime factors of 64314 are 2, 3, 397. Prime factorization of 64314 in exponential form is:

64314 = 2¹ × 3⁴ × 397¹

Step-2: Prime Factorization of 64320

Prime factors of 64320 are 2, 3, 5, 67. Prime factorization of 64320 in exponential form is:

64320 = 2⁶ × 3¹ × 5¹ × 67¹

Step-3: Factors of 64314

List of positive integer factors of 64314 that divides 64314 without a remainder.

1, 2, 3, 6, 9, 18, 27, 54, 81, 162, 397, 794, 1191, 2382, 3573, 7146, 10719, 21438, 32157

Step-4: Factors of 64320

List of positive integer factors of 64320 that divides 64314 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 67, 80, 96, 120, 134, 160, 192, 201, 240, 268, 320, 335, 402, 480, 536, 670, 804, 960, 1005, 1072, 1340, 1608, 2010, 2144, 2680, 3216, 4020, 4288, 5360, 6432, 8040, 10720, 12864, 16080, 21440, 32160

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 64314 and 64320. The biggest common factor number is the GCF number.
So the greatest common factor 64314 and 64320 is 6.

Also check out the Least Common Multiple of 64314 and 64320