What is the Greatest Common Factor of 75735 and 75746?

Greatest common factor (GCF) of 75735 and 75746 is 11.

GCF(75735,75746) = 11

We will now calculate the prime factors of 75735 and 75746, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75735 and 75746.

How to find the GCF of 75735 and 75746?

We will first find the prime factorization of 75735 and 75746. After we will calculate the factors of 75735 and 75746 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 75746

Prime factors of 75746 are 2, 11, 313. Prime factorization of 75746 in exponential form is:

75746 = 2¹ × 11² × 313¹

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 75746

List of positive integer factors of 75746 that divides 75735 without a remainder.

1, 2, 11, 22, 121, 242, 313, 626, 3443, 6886, 37873

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75735 and 75746. The biggest common factor number is the GCF number.
So the greatest common factor 75735 and 75746 is 11.

Also check out the Least Common Multiple of 75735 and 75746