What is the Greatest Common Factor of 66729 and 66744?

Greatest common factor (GCF) of 66729 and 66744 is 3.

GCF(66729,66744) = 3

We will now calculate the prime factors of 66729 and 66744, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 66729 and 66744.

How to find the GCF of 66729 and 66744?

We will first find the prime factorization of 66729 and 66744. After we will calculate the factors of 66729 and 66744 and find the biggest common factor number .

Step-1: Prime Factorization of 66729

Prime factors of 66729 are 3, 13, 29, 59. Prime factorization of 66729 in exponential form is:

66729 = 3¹ × 13¹ × 29¹ × 59¹

Step-2: Prime Factorization of 66744

Prime factors of 66744 are 2, 3, 103. Prime factorization of 66744 in exponential form is:

66744 = 2³ × 3⁴ × 103¹

Step-3: Factors of 66729

List of positive integer factors of 66729 that divides 66729 without a remainder.

1, 3, 13, 29, 39, 59, 87, 177, 377, 767, 1131, 1711, 2301, 5133, 22243

Step-4: Factors of 66744

List of positive integer factors of 66744 that divides 66729 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 103, 108, 162, 206, 216, 309, 324, 412, 618, 648, 824, 927, 1236, 1854, 2472, 2781, 3708, 5562, 7416, 8343, 11124, 16686, 22248, 33372

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 66729 and 66744. The biggest common factor number is the GCF number.
So the greatest common factor 66729 and 66744 is 3.

Also check out the Least Common Multiple of 66729 and 66744