What is the Greatest Common Factor of 85708 and 85722?

Greatest common factor (GCF) of 85708 and 85722 is 14.

GCF(85708,85722) = 14

We will now calculate the prime factors of 85708 and 85722, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 85708 and 85722.

How to find the GCF of 85708 and 85722?

We will first find the prime factorization of 85708 and 85722. After we will calculate the factors of 85708 and 85722 and find the biggest common factor number .

Step-1: Prime Factorization of 85708

Prime factors of 85708 are 2, 7, 3061. Prime factorization of 85708 in exponential form is:

85708 = 2² × 7¹ × 3061¹

Step-2: Prime Factorization of 85722

Prime factors of 85722 are 2, 3, 7, 13, 157. Prime factorization of 85722 in exponential form is:

85722 = 2¹ × 3¹ × 7¹ × 13¹ × 157¹

Step-3: Factors of 85708

List of positive integer factors of 85708 that divides 85708 without a remainder.

1, 2, 4, 7, 14, 28, 3061, 6122, 12244, 21427, 42854

Step-4: Factors of 85722

List of positive integer factors of 85722 that divides 85708 without a remainder.

1, 2, 3, 6, 7, 13, 14, 21, 26, 39, 42, 78, 91, 157, 182, 273, 314, 471, 546, 942, 1099, 2041, 2198, 3297, 4082, 6123, 6594, 12246, 14287, 28574, 42861

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 85708 and 85722. The biggest common factor number is the GCF number.
So the greatest common factor 85708 and 85722 is 14.

Also check out the Least Common Multiple of 85708 and 85722