What is the Greatest Common Factor of 85824 and 85839?

Greatest common factor (GCF) of 85824 and 85839 is 3.

GCF(85824,85839) = 3

We will now calculate the prime factors of 85824 and 85839, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 85824 and 85839.

How to find the GCF of 85824 and 85839?

We will first find the prime factorization of 85824 and 85839. After we will calculate the factors of 85824 and 85839 and find the biggest common factor number .

Step-1: Prime Factorization of 85824

Prime factors of 85824 are 2, 3, 149. Prime factorization of 85824 in exponential form is:

85824 = 2⁶ × 3² × 149¹

Step-2: Prime Factorization of 85839

Prime factors of 85839 are 3, 13, 31, 71. Prime factorization of 85839 in exponential form is:

85839 = 3¹ × 13¹ × 31¹ × 71¹

Step-3: Factors of 85824

List of positive integer factors of 85824 that divides 85824 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 144, 149, 192, 288, 298, 447, 576, 596, 894, 1192, 1341, 1788, 2384, 2682, 3576, 4768, 5364, 7152, 9536, 10728, 14304, 21456, 28608, 42912

Step-4: Factors of 85839

List of positive integer factors of 85839 that divides 85824 without a remainder.

1, 3, 13, 31, 39, 71, 93, 213, 403, 923, 1209, 2201, 2769, 6603, 28613

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 85824 and 85839. The biggest common factor number is the GCF number.
So the greatest common factor 85824 and 85839 is 3.

Also check out the Least Common Multiple of 85824 and 85839