What is the Greatest Common Factor of 85824 and 85840?

Greatest common factor (GCF) of 85824 and 85840 is 16.

GCF(85824,85840) = 16

We will now calculate the prime factors of 85824 and 85840, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 85824 and 85840.

How to find the GCF of 85824 and 85840?

We will first find the prime factorization of 85824 and 85840. After we will calculate the factors of 85824 and 85840 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 85840

Prime factors of 85840 are 2, 5, 29, 37. Prime factorization of 85840 in exponential form is:

85840 = 2⁴ × 5¹ × 29¹ × 37¹

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 85840

List of positive integer factors of 85840 that divides 85824 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 29, 37, 40, 58, 74, 80, 116, 145, 148, 185, 232, 290, 296, 370, 464, 580, 592, 740, 1073, 1160, 1480, 2146, 2320, 2960, 4292, 5365, 8584, 10730, 17168, 21460, 42920

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 85824 and 85840. The biggest common factor number is the GCF number.
So the greatest common factor 85824 and 85840 is 16.

Also check out the Least Common Multiple of 85824 and 85840