What is the Greatest Common Factor of 85709 and 85722?

Greatest common factor (GCF) of 85709 and 85722 is 13.

GCF(85709,85722) = 13

We will now calculate the prime factors of 85709 and 85722, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 85709 and 85722.

How to find the GCF of 85709 and 85722?

We will first find the prime factorization of 85709 and 85722. After we will calculate the factors of 85709 and 85722 and find the biggest common factor number .

Step-1: Prime Factorization of 85709

Prime factors of 85709 are 13, 19, 347. Prime factorization of 85709 in exponential form is:

85709 = 13¹ × 19¹ × 347¹

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 85709

List of positive integer factors of 85709 that divides 85709 without a remainder.

1, 13, 19, 247, 347, 4511, 6593

Step-4: Factors of 85722

List of positive integer factors of 85722 that divides 85709 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 85709 and 85722. The biggest common factor number is the GCF number.
So the greatest common factor 85709 and 85722 is 13.

Also check out the Least Common Multiple of 85709 and 85722