What is the Greatest Common Factor of 36729 and 36736?

Greatest common factor (GCF) of 36729 and 36736 is 7.

GCF(36729,36736) = 7

We will now calculate the prime factors of 36729 and 36736, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 36729 and 36736.

How to find the GCF of 36729 and 36736?

We will first find the prime factorization of 36729 and 36736. After we will calculate the factors of 36729 and 36736 and find the biggest common factor number .

Step-1: Prime Factorization of 36729

Prime factors of 36729 are 3, 7, 11, 53. Prime factorization of 36729 in exponential form is:

36729 = 3² × 7¹ × 11¹ × 53¹

Step-2: Prime Factorization of 36736

Prime factors of 36736 are 2, 7, 41. Prime factorization of 36736 in exponential form is:

36736 = 2⁷ × 7¹ × 41¹

Step-3: Factors of 36729

List of positive integer factors of 36729 that divides 36729 without a remainder.

1, 3, 7, 9, 11, 21, 33, 53, 63, 77, 99, 159, 231, 371, 477, 583, 693, 1113, 1749, 3339, 4081, 5247, 12243

Step-4: Factors of 36736

List of positive integer factors of 36736 that divides 36729 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 32, 41, 56, 64, 82, 112, 128, 164, 224, 287, 328, 448, 574, 656, 896, 1148, 1312, 2296, 2624, 4592, 5248, 9184, 18368

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 36729 and 36736. The biggest common factor number is the GCF number.
So the greatest common factor 36729 and 36736 is 7.

Also check out the Least Common Multiple of 36729 and 36736