What is the Greatest Common Factor of 65728 and 65744?

Greatest common factor (GCF) of 65728 and 65744 is 16.

GCF(65728,65744) = 16

We will now calculate the prime factors of 65728 and 65744, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 65728 and 65744.

How to find the GCF of 65728 and 65744?

We will first find the prime factorization of 65728 and 65744. After we will calculate the factors of 65728 and 65744 and find the biggest common factor number .

Step-1: Prime Factorization of 65728

Prime factors of 65728 are 2, 13, 79. Prime factorization of 65728 in exponential form is:

65728 = 2⁶ × 13¹ × 79¹

Step-2: 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-3: Factors of 65728

List of positive integer factors of 65728 that divides 65728 without a remainder.

1, 2, 4, 8, 13, 16, 26, 32, 52, 64, 79, 104, 158, 208, 316, 416, 632, 832, 1027, 1264, 2054, 2528, 4108, 5056, 8216, 16432, 32864

Step-4: Factors of 65744

List of positive integer factors of 65744 that divides 65728 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 65728 and 65744. The biggest common factor number is the GCF number.
So the greatest common factor 65728 and 65744 is 16.

Also check out the Least Common Multiple of 65728 and 65744