What is the Greatest Common Factor of 32760 and 32767?

Greatest common factor (GCF) of 32760 and 32767 is 7.

GCF(32760,32767) = 7

We will now calculate the prime factors of 32760 and 32767, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 32760 and 32767.

How to find the GCF of 32760 and 32767?

We will first find the prime factorization of 32760 and 32767. After we will calculate the factors of 32760 and 32767 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 32767

Prime factors of 32767 are 7, 31, 151. Prime factorization of 32767 in exponential form is:

32767 = 7¹ × 31¹ × 151¹

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 32767

List of positive integer factors of 32767 that divides 32760 without a remainder.

1, 7, 31, 151, 217, 1057, 4681

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 32760 and 32767. The biggest common factor number is the GCF number.
So the greatest common factor 32760 and 32767 is 7.

Also check out the Least Common Multiple of 32760 and 32767