What is the Greatest Common Factor of 65728 and 65742?

Greatest common factor (GCF) of 65728 and 65742 is 2.

GCF(65728,65742) = 2

We will now calculate the prime factors of 65728 and 65742, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 65728 and 65742.

How to find the GCF of 65728 and 65742?

We will first find the prime factorization of 65728 and 65742. After we will calculate the factors of 65728 and 65742 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 65742

Prime factors of 65742 are 2, 3, 10957. Prime factorization of 65742 in exponential form is:

65742 = 2¹ × 3¹ × 10957¹

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 65742

List of positive integer factors of 65742 that divides 65728 without a remainder.

1, 2, 3, 6, 10957, 21914, 32871

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 65728 and 65742. The biggest common factor number is the GCF number.
So the greatest common factor 65728 and 65742 is 2.

Also check out the Least Common Multiple of 65728 and 65742