What is the Greatest Common Factor of 41744 and 41760?

Greatest common factor (GCF) of 41744 and 41760 is 16.

GCF(41744,41760) = 16

We will now calculate the prime factors of 41744 and 41760, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 41744 and 41760.

How to find the GCF of 41744 and 41760?

We will first find the prime factorization of 41744 and 41760. After we will calculate the factors of 41744 and 41760 and find the biggest common factor number .

Step-1: Prime Factorization of 41744

Prime factors of 41744 are 2, 2609. Prime factorization of 41744 in exponential form is:

41744 = 2⁴ × 2609¹

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 41744

List of positive integer factors of 41744 that divides 41744 without a remainder.

1, 2, 4, 8, 16, 2609, 5218, 10436, 20872

Step-4: Factors of 41760

List of positive integer factors of 41760 that divides 41744 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 41744 and 41760. The biggest common factor number is the GCF number.
So the greatest common factor 41744 and 41760 is 16.

Also check out the Least Common Multiple of 41744 and 41760