What is the Greatest Common Factor of 85782 and 85800?

Greatest common factor (GCF) of 85782 and 85800 is 6.

GCF(85782,85800) = 6

We will now calculate the prime factors of 85782 and 85800, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 85782 and 85800.

How to find the GCF of 85782 and 85800?

We will first find the prime factorization of 85782 and 85800. After we will calculate the factors of 85782 and 85800 and find the biggest common factor number .

Step-1: Prime Factorization of 85782

Prime factors of 85782 are 2, 3, 17, 29. Prime factorization of 85782 in exponential form is:

85782 = 2¹ × 3¹ × 17¹ × 29²

Step-2: Prime Factorization of 85800

Prime factors of 85800 are 2, 3, 5, 11, 13. Prime factorization of 85800 in exponential form is:

85800 = 2³ × 3¹ × 5² × 11¹ × 13¹

Step-3: Factors of 85782

List of positive integer factors of 85782 that divides 85782 without a remainder.

1, 2, 3, 6, 17, 29, 34, 51, 58, 87, 102, 174, 493, 841, 986, 1479, 1682, 2523, 2958, 5046, 14297, 28594, 42891

Step-4: Factors of 85800

List of positive integer factors of 85800 that divides 85782 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 13, 15, 20, 22, 24, 25, 26, 30, 33, 39, 40, 44, 50, 52, 55, 60, 65, 66, 75, 78, 88, 100, 104, 110, 120, 130, 132, 143, 150, 156, 165, 195, 200, 220, 260, 264, 275, 286, 300, 312, 325, 330, 390, 429, 440, 520, 550, 572, 600, 650, 660, 715, 780, 825, 858, 975, 1100, 1144, 1300, 1320, 1430, 1560, 1650, 1716, 1950, 2145, 2200, 2600, 2860, 3300, 3432, 3575, 3900, 4290, 5720, 6600, 7150, 7800, 8580, 10725, 14300, 17160, 21450, 28600, 42900

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 85782 and 85800. The biggest common factor number is the GCF number.
So the greatest common factor 85782 and 85800 is 6.

Also check out the Least Common Multiple of 85782 and 85800