What is the Greatest Common Factor of 51345 and 51360?

Greatest common factor (GCF) of 51345 and 51360 is 15.

GCF(51345,51360) = 15

We will now calculate the prime factors of 51345 and 51360, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 51345 and 51360.

How to find the GCF of 51345 and 51360?

We will first find the prime factorization of 51345 and 51360. After we will calculate the factors of 51345 and 51360 and find the biggest common factor number .

Step-1: Prime Factorization of 51345

Prime factors of 51345 are 3, 5, 7, 163. Prime factorization of 51345 in exponential form is:

51345 = 3² × 5¹ × 7¹ × 163¹

Step-2: Prime Factorization of 51360

Prime factors of 51360 are 2, 3, 5, 107. Prime factorization of 51360 in exponential form is:

51360 = 2⁵ × 3¹ × 5¹ × 107¹

Step-3: Factors of 51345

List of positive integer factors of 51345 that divides 51345 without a remainder.

1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, 163, 315, 489, 815, 1141, 1467, 2445, 3423, 5705, 7335, 10269, 17115

Step-4: Factors of 51360

List of positive integer factors of 51360 that divides 51345 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 80, 96, 107, 120, 160, 214, 240, 321, 428, 480, 535, 642, 856, 1070, 1284, 1605, 1712, 2140, 2568, 3210, 3424, 4280, 5136, 6420, 8560, 10272, 12840, 17120, 25680

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 51345 and 51360. The biggest common factor number is the GCF number.
So the greatest common factor 51345 and 51360 is 15.

Also check out the Least Common Multiple of 51345 and 51360