What is the Greatest Common Factor of 17754 and 17760?

Greatest common factor (GCF) of 17754 and 17760 is 6.

GCF(17754,17760) = 6

We will now calculate the prime factors of 17754 and 17760, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17754 and 17760.

How to find the GCF of 17754 and 17760?

We will first find the prime factorization of 17754 and 17760. After we will calculate the factors of 17754 and 17760 and find the biggest common factor number .

Step-1: Prime Factorization of 17754

Prime factors of 17754 are 2, 3, 11, 269. Prime factorization of 17754 in exponential form is:

17754 = 2¹ × 3¹ × 11¹ × 269¹

Step-2: Prime Factorization of 17760

Prime factors of 17760 are 2, 3, 5, 37. Prime factorization of 17760 in exponential form is:

17760 = 2⁵ × 3¹ × 5¹ × 37¹

Step-3: Factors of 17754

List of positive integer factors of 17754 that divides 17754 without a remainder.

1, 2, 3, 6, 11, 22, 33, 66, 269, 538, 807, 1614, 2959, 5918, 8877

Step-4: Factors of 17760

List of positive integer factors of 17760 that divides 17754 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 37, 40, 48, 60, 74, 80, 96, 111, 120, 148, 160, 185, 222, 240, 296, 370, 444, 480, 555, 592, 740, 888, 1110, 1184, 1480, 1776, 2220, 2960, 3552, 4440, 5920, 8880

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17754 and 17760. The biggest common factor number is the GCF number.
So the greatest common factor 17754 and 17760 is 6.

Also check out the Least Common Multiple of 17754 and 17760