What is the Greatest Common Factor of 71586 and 71604?

Greatest common factor (GCF) of 71586 and 71604 is 18.

GCF(71586,71604) = 18

We will now calculate the prime factors of 71586 and 71604, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 71586 and 71604.

How to find the GCF of 71586 and 71604?

We will first find the prime factorization of 71586 and 71604. After we will calculate the factors of 71586 and 71604 and find the biggest common factor number .

Step-1: Prime Factorization of 71586

Prime factors of 71586 are 2, 3, 41, 97. Prime factorization of 71586 in exponential form is:

71586 = 2¹ × 3² × 41¹ × 97¹

Step-2: Prime Factorization of 71604

Prime factors of 71604 are 2, 3, 13, 17. Prime factorization of 71604 in exponential form is:

71604 = 2² × 3⁴ × 13¹ × 17¹

Step-3: Factors of 71586

List of positive integer factors of 71586 that divides 71586 without a remainder.

1, 2, 3, 6, 9, 18, 41, 82, 97, 123, 194, 246, 291, 369, 582, 738, 873, 1746, 3977, 7954, 11931, 23862, 35793

Step-4: Factors of 71604

List of positive integer factors of 71604 that divides 71586 without a remainder.

1, 2, 3, 4, 6, 9, 12, 13, 17, 18, 26, 27, 34, 36, 39, 51, 52, 54, 68, 78, 81, 102, 108, 117, 153, 156, 162, 204, 221, 234, 306, 324, 351, 442, 459, 468, 612, 663, 702, 884, 918, 1053, 1326, 1377, 1404, 1836, 1989, 2106, 2652, 2754, 3978, 4212, 5508, 5967, 7956, 11934, 17901, 23868, 35802

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 71586 and 71604. The biggest common factor number is the GCF number.
So the greatest common factor 71586 and 71604 is 18.

Also check out the Least Common Multiple of 71586 and 71604