What is the Greatest Common Factor of 32760 and 32766?

Greatest common factor (GCF) of 32760 and 32766 is 6.

GCF(32760,32766) = 6

We will now calculate the prime factors of 32760 and 32766, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 32760 and 32766.

How to find the GCF of 32760 and 32766?

We will first find the prime factorization of 32760 and 32766. After we will calculate the factors of 32760 and 32766 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 32766

Prime factors of 32766 are 2, 3, 43, 127. Prime factorization of 32766 in exponential form is:

32766 = 2¹ × 3¹ × 43¹ × 127¹

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 32766

List of positive integer factors of 32766 that divides 32760 without a remainder.

1, 2, 3, 6, 43, 86, 127, 129, 254, 258, 381, 762, 5461, 10922, 16383

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 32760 and 32766. The biggest common factor number is the GCF number.
So the greatest common factor 32760 and 32766 is 6.

Also check out the Least Common Multiple of 32760 and 32766