What is the Greatest Common Factor of 85712 and 85728?

Greatest common factor (GCF) of 85712 and 85728 is 16.

GCF(85712,85728) = 16

We will now calculate the prime factors of 85712 and 85728, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 85712 and 85728.

How to find the GCF of 85712 and 85728?

We will first find the prime factorization of 85712 and 85728. After we will calculate the factors of 85712 and 85728 and find the biggest common factor number .

Step-1: Prime Factorization of 85712

Prime factors of 85712 are 2, 11, 487. Prime factorization of 85712 in exponential form is:

85712 = 2⁴ × 11¹ × 487¹

Step-2: Prime Factorization of 85728

Prime factors of 85728 are 2, 3, 19, 47. Prime factorization of 85728 in exponential form is:

85728 = 2⁵ × 3¹ × 19¹ × 47¹

Step-3: Factors of 85712

List of positive integer factors of 85712 that divides 85712 without a remainder.

1, 2, 4, 8, 11, 16, 22, 44, 88, 176, 487, 974, 1948, 3896, 5357, 7792, 10714, 21428, 42856

Step-4: Factors of 85728

List of positive integer factors of 85728 that divides 85712 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 19, 24, 32, 38, 47, 48, 57, 76, 94, 96, 114, 141, 152, 188, 228, 282, 304, 376, 456, 564, 608, 752, 893, 912, 1128, 1504, 1786, 1824, 2256, 2679, 3572, 4512, 5358, 7144, 10716, 14288, 21432, 28576, 42864

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 85712 and 85728. The biggest common factor number is the GCF number.
So the greatest common factor 85712 and 85728 is 16.

Also check out the Least Common Multiple of 85712 and 85728