What is the Greatest Common Factor of 75724 and 75735?

Greatest common factor (GCF) of 75724 and 75735 is 11.

GCF(75724,75735) = 11

We will now calculate the prime factors of 75724 and 75735, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75724 and 75735.

How to find the GCF of 75724 and 75735?

We will first find the prime factorization of 75724 and 75735. After we will calculate the factors of 75724 and 75735 and find the biggest common factor number .

Step-1: Prime Factorization of 75724

Prime factors of 75724 are 2, 11, 1721. Prime factorization of 75724 in exponential form is:

75724 = 2² × 11¹ × 1721¹

Step-2: 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-3: Factors of 75724

List of positive integer factors of 75724 that divides 75724 without a remainder.

1, 2, 4, 11, 22, 44, 1721, 3442, 6884, 18931, 37862

Step-4: Factors of 75735

List of positive integer factors of 75735 that divides 75724 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75724 and 75735. The biggest common factor number is the GCF number.
So the greatest common factor 75724 and 75735 is 11.

Also check out the Least Common Multiple of 75724 and 75735