What is the Greatest Common Factor of 85872 and 85888?

Greatest common factor (GCF) of 85872 and 85888 is 16.

GCF(85872,85888) = 16

We will now calculate the prime factors of 85872 and 85888, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 85872 and 85888.

How to find the GCF of 85872 and 85888?

We will first find the prime factorization of 85872 and 85888. After we will calculate the factors of 85872 and 85888 and find the biggest common factor number .

Step-1: Prime Factorization of 85872

Prime factors of 85872 are 2, 3, 1789. Prime factorization of 85872 in exponential form is:

85872 = 2⁴ × 3¹ × 1789¹

Step-2: Prime Factorization of 85888

Prime factors of 85888 are 2, 11, 61. Prime factorization of 85888 in exponential form is:

85888 = 2⁷ × 11¹ × 61¹

Step-3: Factors of 85872

List of positive integer factors of 85872 that divides 85872 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 1789, 3578, 5367, 7156, 10734, 14312, 21468, 28624, 42936

Step-4: Factors of 85888

List of positive integer factors of 85888 that divides 85872 without a remainder.

1, 2, 4, 8, 11, 16, 22, 32, 44, 61, 64, 88, 122, 128, 176, 244, 352, 488, 671, 704, 976, 1342, 1408, 1952, 2684, 3904, 5368, 7808, 10736, 21472, 42944

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 85872 and 85888. The biggest common factor number is the GCF number.
So the greatest common factor 85872 and 85888 is 16.

Also check out the Least Common Multiple of 85872 and 85888