What is the Greatest Common Factor of 85824 and 85842?

Greatest common factor (GCF) of 85824 and 85842 is 18.

GCF(85824,85842) = 18

We will now calculate the prime factors of 85824 and 85842, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 85824 and 85842.

How to find the GCF of 85824 and 85842?

We will first find the prime factorization of 85824 and 85842. After we will calculate the factors of 85824 and 85842 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 85842

Prime factors of 85842 are 2, 3, 19, 251. Prime factorization of 85842 in exponential form is:

85842 = 2¹ × 3² × 19¹ × 251¹

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 85842

List of positive integer factors of 85842 that divides 85824 without a remainder.

1, 2, 3, 6, 9, 18, 19, 38, 57, 114, 171, 251, 342, 502, 753, 1506, 2259, 4518, 4769, 9538, 14307, 28614, 42921

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 85824 and 85842. The biggest common factor number is the GCF number.
So the greatest common factor 85824 and 85842 is 18.

Also check out the Least Common Multiple of 85824 and 85842