What is the Greatest Common Factor of 39728 and 39742?

Greatest common factor (GCF) of 39728 and 39742 is 2.

GCF(39728,39742) = 2

We will now calculate the prime factors of 39728 and 39742, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39728 and 39742.

How to find the GCF of 39728 and 39742?

We will first find the prime factorization of 39728 and 39742. After we will calculate the factors of 39728 and 39742 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 39742

Prime factors of 39742 are 2, 31, 641. Prime factorization of 39742 in exponential form is:

39742 = 2¹ × 31¹ × 641¹

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 39742

List of positive integer factors of 39742 that divides 39728 without a remainder.

1, 2, 31, 62, 641, 1282, 19871

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39728 and 39742. The biggest common factor number is the GCF number.
So the greatest common factor 39728 and 39742 is 2.

Also check out the Least Common Multiple of 39728 and 39742