What is the Greatest Common Factor of 75735 and 75752?

Greatest common factor (GCF) of 75735 and 75752 is 17.

GCF(75735,75752) = 17

We will now calculate the prime factors of 75735 and 75752, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75735 and 75752.

How to find the GCF of 75735 and 75752?

We will first find the prime factorization of 75735 and 75752. After we will calculate the factors of 75735 and 75752 and find the biggest common factor number .

Step-1: Prime Factorization of 75735

Prime factors of 75735 are 3, 5, 11, 17. Prime factorization of 75735 in exponential form is:

75735 = 3⁴ × 5¹ × 11¹ × 17¹

Step-2: Prime Factorization of 75752

Prime factors of 75752 are 2, 17, 557. Prime factorization of 75752 in exponential form is:

75752 = 2³ × 17¹ × 557¹

Step-3: Factors of 75735

List of positive integer factors of 75735 that divides 75735 without a remainder.

1, 3, 5, 9, 11, 15, 17, 27, 33, 45, 51, 55, 81, 85, 99, 135, 153, 165, 187, 255, 297, 405, 459, 495, 561, 765, 891, 935, 1377, 1485, 1683, 2295, 2805, 4455, 5049, 6885, 8415, 15147, 25245

Step-4: Factors of 75752

List of positive integer factors of 75752 that divides 75735 without a remainder.

1, 2, 4, 8, 17, 34, 68, 136, 557, 1114, 2228, 4456, 9469, 18938, 37876

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75735 and 75752. The biggest common factor number is the GCF number.
So the greatest common factor 75735 and 75752 is 17.

Also check out the Least Common Multiple of 75735 and 75752