What is the Greatest Common Factor of 41742 and 41760?

Greatest common factor (GCF) of 41742 and 41760 is 18.

GCF(41742,41760) = 18

We will now calculate the prime factors of 41742 and 41760, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 41742 and 41760.

How to find the GCF of 41742 and 41760?

We will first find the prime factorization of 41742 and 41760. After we will calculate the factors of 41742 and 41760 and find the biggest common factor number .

Step-1: Prime Factorization of 41742

Prime factors of 41742 are 2, 3, 773. Prime factorization of 41742 in exponential form is:

41742 = 2¹ × 3³ × 773¹

Step-2: Prime Factorization of 41760

Prime factors of 41760 are 2, 3, 5, 29. Prime factorization of 41760 in exponential form is:

41760 = 2⁵ × 3² × 5¹ × 29¹

Step-3: Factors of 41742

List of positive integer factors of 41742 that divides 41742 without a remainder.

1, 2, 3, 6, 9, 18, 27, 54, 773, 1546, 2319, 4638, 6957, 13914, 20871

Step-4: Factors of 41760

List of positive integer factors of 41760 that divides 41742 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 29, 30, 32, 36, 40, 45, 48, 58, 60, 72, 80, 87, 90, 96, 116, 120, 144, 145, 160, 174, 180, 232, 240, 261, 288, 290, 348, 360, 435, 464, 480, 522, 580, 696, 720, 870, 928, 1044, 1160, 1305, 1392, 1440, 1740, 2088, 2320, 2610, 2784, 3480, 4176, 4640, 5220, 6960, 8352, 10440, 13920, 20880

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 41742 and 41760. The biggest common factor number is the GCF number.
So the greatest common factor 41742 and 41760 is 18.

Also check out the Least Common Multiple of 41742 and 41760