What is the Greatest Common Factor of 65709 and 65728?

Greatest common factor (GCF) of 65709 and 65728 is 1.

GCF(65709,65728) = 1

We will now calculate the prime factors of 65709 and 65728, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 65709 and 65728.

How to find the GCF of 65709 and 65728?

We will first find the prime factorization of 65709 and 65728. After we will calculate the factors of 65709 and 65728 and find the biggest common factor number .

Step-1: Prime Factorization of 65709

Prime factors of 65709 are 3, 7, 149. Prime factorization of 65709 in exponential form is:

65709 = 3² × 7² × 149¹

Step-2: 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-3: Factors of 65709

List of positive integer factors of 65709 that divides 65709 without a remainder.

1, 3, 7, 9, 21, 49, 63, 147, 149, 441, 447, 1043, 1341, 3129, 7301, 9387, 21903

Step-4: Factors of 65728

List of positive integer factors of 65728 that divides 65709 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 65709 and 65728. The biggest common factor number is the GCF number.
So the greatest common factor 65709 and 65728 is 1.

Also check out the Least Common Multiple of 65709 and 65728