What is the Greatest Common Factor of 65744 and 65760?

Greatest common factor (GCF) of 65744 and 65760 is 16.

GCF(65744,65760) = 16

We will now calculate the prime factors of 65744 and 65760, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 65744 and 65760.

How to find the GCF of 65744 and 65760?

We will first find the prime factorization of 65744 and 65760. After we will calculate the factors of 65744 and 65760 and find the biggest common factor number .

Step-1: Prime Factorization of 65744

Prime factors of 65744 are 2, 7, 587. Prime factorization of 65744 in exponential form is:

65744 = 2⁴ × 7¹ × 587¹

Step-2: Prime Factorization of 65760

Prime factors of 65760 are 2, 3, 5, 137. Prime factorization of 65760 in exponential form is:

65760 = 2⁵ × 3¹ × 5¹ × 137¹

Step-3: Factors of 65744

List of positive integer factors of 65744 that divides 65744 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 56, 112, 587, 1174, 2348, 4109, 4696, 8218, 9392, 16436, 32872

Step-4: Factors of 65760

List of positive integer factors of 65760 that divides 65744 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 80, 96, 120, 137, 160, 240, 274, 411, 480, 548, 685, 822, 1096, 1370, 1644, 2055, 2192, 2740, 3288, 4110, 4384, 5480, 6576, 8220, 10960, 13152, 16440, 21920, 32880

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 65744 and 65760. The biggest common factor number is the GCF number.
So the greatest common factor 65744 and 65760 is 16.

Also check out the Least Common Multiple of 65744 and 65760