What is the Greatest Common Factor of 85800 and 85813?

Greatest common factor (GCF) of 85800 and 85813 is 13.

GCF(85800,85813) = 13

We will now calculate the prime factors of 85800 and 85813, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 85800 and 85813.

How to find the GCF of 85800 and 85813?

We will first find the prime factorization of 85800 and 85813. After we will calculate the factors of 85800 and 85813 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 85813

Prime factors of 85813 are 7, 13, 23, 41. Prime factorization of 85813 in exponential form is:

85813 = 7¹ × 13¹ × 23¹ × 41¹

Step-3: Factors of 85800

List of positive integer factors of 85800 that divides 85800 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

Step-4: Factors of 85813

List of positive integer factors of 85813 that divides 85800 without a remainder.

1, 7, 13, 23, 41, 91, 161, 287, 299, 533, 943, 2093, 3731, 6601, 12259

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 85800 and 85813. The biggest common factor number is the GCF number.
So the greatest common factor 85800 and 85813 is 13.

Also check out the Least Common Multiple of 85800 and 85813