What is the Greatest Common Factor of 39728 and 39732?

Greatest common factor (GCF) of 39728 and 39732 is 4.

GCF(39728,39732) = 4

We will now calculate the prime factors of 39728 and 39732, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39728 and 39732.

How to find the GCF of 39728 and 39732?

We will first find the prime factorization of 39728 and 39732. After we will calculate the factors of 39728 and 39732 and find the biggest common factor number .

Step-1: Prime Factorization of 39728

Prime factors of 39728 are 2, 13, 191. Prime factorization of 39728 in exponential form is:

39728 = 2⁴ × 13¹ × 191¹

Step-2: Prime Factorization of 39732

Prime factors of 39732 are 2, 3, 7, 11, 43. Prime factorization of 39732 in exponential form is:

39732 = 2² × 3¹ × 7¹ × 11¹ × 43¹

Step-3: Factors of 39728

List of positive integer factors of 39728 that divides 39728 without a remainder.

1, 2, 4, 8, 13, 16, 26, 52, 104, 191, 208, 382, 764, 1528, 2483, 3056, 4966, 9932, 19864

Step-4: Factors of 39732

List of positive integer factors of 39732 that divides 39728 without a remainder.

1, 2, 3, 4, 6, 7, 11, 12, 14, 21, 22, 28, 33, 42, 43, 44, 66, 77, 84, 86, 129, 132, 154, 172, 231, 258, 301, 308, 462, 473, 516, 602, 903, 924, 946, 1204, 1419, 1806, 1892, 2838, 3311, 3612, 5676, 6622, 9933, 13244, 19866

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39728 and 39732. The biggest common factor number is the GCF number.
So the greatest common factor 39728 and 39732 is 4.

Also check out the Least Common Multiple of 39728 and 39732