What is the Greatest Common Factor of 15738 and 15744?

Greatest common factor (GCF) of 15738 and 15744 is 6.

GCF(15738,15744) = 6

We will now calculate the prime factors of 15738 and 15744, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 15738 and 15744.

How to find the GCF of 15738 and 15744?

We will first find the prime factorization of 15738 and 15744. After we will calculate the factors of 15738 and 15744 and find the biggest common factor number .

Step-1: Prime Factorization of 15738

Prime factors of 15738 are 2, 3, 43, 61. Prime factorization of 15738 in exponential form is:

15738 = 2¹ × 3¹ × 43¹ × 61¹

Step-2: Prime Factorization of 15744

Prime factors of 15744 are 2, 3, 41. Prime factorization of 15744 in exponential form is:

15744 = 2⁷ × 3¹ × 41¹

Step-3: Factors of 15738

List of positive integer factors of 15738 that divides 15738 without a remainder.

1, 2, 3, 6, 43, 61, 86, 122, 129, 183, 258, 366, 2623, 5246, 7869

Step-4: Factors of 15744

List of positive integer factors of 15744 that divides 15738 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 41, 48, 64, 82, 96, 123, 128, 164, 192, 246, 328, 384, 492, 656, 984, 1312, 1968, 2624, 3936, 5248, 7872

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 15738 and 15744. The biggest common factor number is the GCF number.
So the greatest common factor 15738 and 15744 is 6.

Also check out the Least Common Multiple of 15738 and 15744