What is the Greatest Common Factor of 75735 and 75750?

Greatest common factor (GCF) of 75735 and 75750 is 15.

GCF(75735,75750) = 15

We will now calculate the prime factors of 75735 and 75750, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75735 and 75750.

How to find the GCF of 75735 and 75750?

We will first find the prime factorization of 75735 and 75750. After we will calculate the factors of 75735 and 75750 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 75750

Prime factors of 75750 are 2, 3, 5, 101. Prime factorization of 75750 in exponential form is:

75750 = 2¹ × 3¹ × 5³ × 101¹

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 75750

List of positive integer factors of 75750 that divides 75735 without a remainder.

1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 101, 125, 150, 202, 250, 303, 375, 505, 606, 750, 1010, 1515, 2525, 3030, 5050, 7575, 12625, 15150, 25250, 37875

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75735 and 75750. The biggest common factor number is the GCF number.
So the greatest common factor 75735 and 75750 is 15.

Also check out the Least Common Multiple of 75735 and 75750