What is the Greatest Common Factor of 85704 and 85722?

Greatest common factor (GCF) of 85704 and 85722 is 6.

GCF(85704,85722) = 6

We will now calculate the prime factors of 85704 and 85722, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 85704 and 85722.

How to find the GCF of 85704 and 85722?

We will first find the prime factorization of 85704 and 85722. After we will calculate the factors of 85704 and 85722 and find the biggest common factor number .

Step-1: Prime Factorization of 85704

Prime factors of 85704 are 2, 3, 3571. Prime factorization of 85704 in exponential form is:

85704 = 2³ × 3¹ × 3571¹

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 85704

List of positive integer factors of 85704 that divides 85704 without a remainder.

1, 2, 3, 4, 6, 8, 12, 24, 3571, 7142, 10713, 14284, 21426, 28568, 42852

Step-4: Factors of 85722

List of positive integer factors of 85722 that divides 85704 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 85704 and 85722. The biggest common factor number is the GCF number.
So the greatest common factor 85704 and 85722 is 6.

Also check out the Least Common Multiple of 85704 and 85722