What is the Greatest Common Factor of 85710 and 85728?

Greatest common factor (GCF) of 85710 and 85728 is 6.

GCF(85710,85728) = 6

We will now calculate the prime factors of 85710 and 85728, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 85710 and 85728.

How to find the GCF of 85710 and 85728?

We will first find the prime factorization of 85710 and 85728. After we will calculate the factors of 85710 and 85728 and find the biggest common factor number .

Step-1: Prime Factorization of 85710

Prime factors of 85710 are 2, 3, 5, 2857. Prime factorization of 85710 in exponential form is:

85710 = 2¹ × 3¹ × 5¹ × 2857¹

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 85710

List of positive integer factors of 85710 that divides 85710 without a remainder.

1, 2, 3, 5, 6, 10, 15, 30, 2857, 5714, 8571, 14285, 17142, 28570, 42855

Step-4: Factors of 85728

List of positive integer factors of 85728 that divides 85710 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 85710 and 85728. The biggest common factor number is the GCF number.
So the greatest common factor 85710 and 85728 is 6.

Also check out the Least Common Multiple of 85710 and 85728