What is the Greatest Common Factor of 32760 and 32775?

Greatest common factor (GCF) of 32760 and 32775 is 15.

GCF(32760,32775) = 15

We will now calculate the prime factors of 32760 and 32775, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 32760 and 32775.

How to find the GCF of 32760 and 32775?

We will first find the prime factorization of 32760 and 32775. After we will calculate the factors of 32760 and 32775 and find the biggest common factor number .

Step-1: Prime Factorization of 32760

Prime factors of 32760 are 2, 3, 5, 7, 13. Prime factorization of 32760 in exponential form is:

32760 = 2³ × 3² × 5¹ × 7¹ × 13¹

Step-2: Prime Factorization of 32775

Prime factors of 32775 are 3, 5, 19, 23. Prime factorization of 32775 in exponential form is:

32775 = 3¹ × 5² × 19¹ × 23¹

Step-3: Factors of 32760

List of positive integer factors of 32760 that divides 32760 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 18, 20, 21, 24, 26, 28, 30, 35, 36, 39, 40, 42, 45, 52, 56, 60, 63, 65, 70, 72, 78, 84, 90, 91, 104, 105, 117, 120, 126, 130, 140, 156, 168, 180, 182, 195, 210, 234, 252, 260, 273, 280, 312, 315, 360, 364, 390, 420, 455, 468, 504, 520, 546, 585, 630, 728, 780, 819, 840, 910, 936, 1092, 1170, 1260, 1365, 1560, 1638, 1820, 2184, 2340, 2520, 2730, 3276, 3640, 4095, 4680, 5460, 6552, 8190, 10920, 16380

Step-4: Factors of 32775

List of positive integer factors of 32775 that divides 32760 without a remainder.

1, 3, 5, 15, 19, 23, 25, 57, 69, 75, 95, 115, 285, 345, 437, 475, 575, 1311, 1425, 1725, 2185, 6555, 10925

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 32760 and 32775. The biggest common factor number is the GCF number.
So the greatest common factor 32760 and 32775 is 15.

Also check out the Least Common Multiple of 32760 and 32775