What is the Greatest Common Factor of 76545 and 76560?

Greatest common factor (GCF) of 76545 and 76560 is 15.

GCF(76545,76560) = 15

We will now calculate the prime factors of 76545 and 76560, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 76545 and 76560.

How to find the GCF of 76545 and 76560?

We will first find the prime factorization of 76545 and 76560. After we will calculate the factors of 76545 and 76560 and find the biggest common factor number .

Step-1: Prime Factorization of 76545

Prime factors of 76545 are 3, 5, 7. Prime factorization of 76545 in exponential form is:

76545 = 3⁷ × 5¹ × 7¹

Step-2: Prime Factorization of 76560

Prime factors of 76560 are 2, 3, 5, 11, 29. Prime factorization of 76560 in exponential form is:

76560 = 2⁴ × 3¹ × 5¹ × 11¹ × 29¹

Step-3: Factors of 76545

List of positive integer factors of 76545 that divides 76545 without a remainder.

1, 3, 5, 7, 9, 15, 21, 27, 35, 45, 63, 81, 105, 135, 189, 243, 315, 405, 567, 729, 945, 1215, 1701, 2187, 2835, 3645, 5103, 8505, 10935, 15309, 25515

Step-4: Factors of 76560

List of positive integer factors of 76560 that divides 76545 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 16, 20, 22, 24, 29, 30, 33, 40, 44, 48, 55, 58, 60, 66, 80, 87, 88, 110, 116, 120, 132, 145, 165, 174, 176, 220, 232, 240, 264, 290, 319, 330, 348, 435, 440, 464, 528, 580, 638, 660, 696, 870, 880, 957, 1160, 1276, 1320, 1392, 1595, 1740, 1914, 2320, 2552, 2640, 3190, 3480, 3828, 4785, 5104, 6380, 6960, 7656, 9570, 12760, 15312, 19140, 25520, 38280

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 76545 and 76560. The biggest common factor number is the GCF number.
So the greatest common factor 76545 and 76560 is 15.

Also check out the Least Common Multiple of 76545 and 76560