What is the Greatest Common Factor of 85664 and 85680?

Greatest common factor (GCF) of 85664 and 85680 is 16.

GCF(85664,85680) = 16

We will now calculate the prime factors of 85664 and 85680, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 85664 and 85680.

How to find the GCF of 85664 and 85680?

We will first find the prime factorization of 85664 and 85680. After we will calculate the factors of 85664 and 85680 and find the biggest common factor number .

Step-1: Prime Factorization of 85664

Prime factors of 85664 are 2, 2677. Prime factorization of 85664 in exponential form is:

85664 = 2⁵ × 2677¹

Step-2: Prime Factorization of 85680

Prime factors of 85680 are 2, 3, 5, 7, 17. Prime factorization of 85680 in exponential form is:

85680 = 2⁴ × 3² × 5¹ × 7¹ × 17¹

Step-3: Factors of 85664

List of positive integer factors of 85664 that divides 85664 without a remainder.

1, 2, 4, 8, 16, 32, 2677, 5354, 10708, 21416, 42832

Step-4: Factors of 85680

List of positive integer factors of 85680 that divides 85664 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 17, 18, 20, 21, 24, 28, 30, 34, 35, 36, 40, 42, 45, 48, 51, 56, 60, 63, 68, 70, 72, 80, 84, 85, 90, 102, 105, 112, 119, 120, 126, 136, 140, 144, 153, 168, 170, 180, 204, 210, 238, 240, 252, 255, 272, 280, 306, 315, 336, 340, 357, 360, 408, 420, 476, 504, 510, 560, 595, 612, 630, 680, 714, 720, 765, 816, 840, 952, 1008, 1020, 1071, 1190, 1224, 1260, 1360, 1428, 1530, 1680, 1785, 1904, 2040, 2142, 2380, 2448, 2520, 2856, 3060, 3570, 4080, 4284, 4760, 5040, 5355, 5712, 6120, 7140, 8568, 9520, 10710, 12240, 14280, 17136, 21420, 28560, 42840

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 85664 and 85680. The biggest common factor number is the GCF number.
So the greatest common factor 85664 and 85680 is 16.

Also check out the Least Common Multiple of 85664 and 85680