What is the Greatest Common Factor of 85674 and 85680?

Greatest common factor (GCF) of 85674 and 85680 is 6.

GCF(85674,85680) = 6

We will now calculate the prime factors of 85674 and 85680, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 85674 and 85680.

How to find the GCF of 85674 and 85680?

We will first find the prime factorization of 85674 and 85680. After we will calculate the factors of 85674 and 85680 and find the biggest common factor number .

Step-1: Prime Factorization of 85674

Prime factors of 85674 are 2, 3, 109, 131. Prime factorization of 85674 in exponential form is:

85674 = 2¹ × 3¹ × 109¹ × 131¹

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 85674

List of positive integer factors of 85674 that divides 85674 without a remainder.

1, 2, 3, 6, 109, 131, 218, 262, 327, 393, 654, 786, 14279, 28558, 42837

Step-4: Factors of 85680

List of positive integer factors of 85680 that divides 85674 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 85674 and 85680. The biggest common factor number is the GCF number.
So the greatest common factor 85674 and 85680 is 6.

Also check out the Least Common Multiple of 85674 and 85680