What is the Greatest Common Factor of 15744 and 15762?

Greatest common factor (GCF) of 15744 and 15762 is 6.

GCF(15744,15762) = 6

We will now calculate the prime factors of 15744 and 15762, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 15744 and 15762.

How to find the GCF of 15744 and 15762?

We will first find the prime factorization of 15744 and 15762. After we will calculate the factors of 15744 and 15762 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 15762

Prime factors of 15762 are 2, 3, 37, 71. Prime factorization of 15762 in exponential form is:

15762 = 2¹ × 3¹ × 37¹ × 71¹

Step-3: Factors of 15744

List of positive integer factors of 15744 that divides 15744 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

Step-4: Factors of 15762

List of positive integer factors of 15762 that divides 15744 without a remainder.

1, 2, 3, 6, 37, 71, 74, 111, 142, 213, 222, 426, 2627, 5254, 7881

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 15744 and 15762. The biggest common factor number is the GCF number.
So the greatest common factor 15744 and 15762 is 6.

Also check out the Least Common Multiple of 15744 and 15762