What is the Greatest Common Factor of 75565 and 75582?

Greatest common factor (GCF) of 75565 and 75582 is 17.

GCF(75565,75582) = 17

We will now calculate the prime factors of 75565 and 75582, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75565 and 75582.

How to find the GCF of 75565 and 75582?

We will first find the prime factorization of 75565 and 75582. After we will calculate the factors of 75565 and 75582 and find the biggest common factor number .

Step-1: Prime Factorization of 75565

Prime factors of 75565 are 5, 7, 17, 127. Prime factorization of 75565 in exponential form is:

75565 = 5¹ × 7¹ × 17¹ × 127¹

Step-2: Prime Factorization of 75582

Prime factors of 75582 are 2, 3, 13, 17, 19. Prime factorization of 75582 in exponential form is:

75582 = 2¹ × 3² × 13¹ × 17¹ × 19¹

Step-3: Factors of 75565

List of positive integer factors of 75565 that divides 75565 without a remainder.

1, 5, 7, 17, 35, 85, 119, 127, 595, 635, 889, 2159, 4445, 10795, 15113

Step-4: Factors of 75582

List of positive integer factors of 75582 that divides 75565 without a remainder.

1, 2, 3, 6, 9, 13, 17, 18, 19, 26, 34, 38, 39, 51, 57, 78, 102, 114, 117, 153, 171, 221, 234, 247, 306, 323, 342, 442, 494, 646, 663, 741, 969, 1326, 1482, 1938, 1989, 2223, 2907, 3978, 4199, 4446, 5814, 8398, 12597, 25194, 37791

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75565 and 75582. The biggest common factor number is the GCF number.
So the greatest common factor 75565 and 75582 is 17.

Also check out the Least Common Multiple of 75565 and 75582