What is the Greatest Common Factor of 19536 and 19542?

Greatest common factor (GCF) of 19536 and 19542 is 6.

GCF(19536,19542) = 6

We will now calculate the prime factors of 19536 and 19542, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19536 and 19542.

How to find the GCF of 19536 and 19542?

We will first find the prime factorization of 19536 and 19542. After we will calculate the factors of 19536 and 19542 and find the biggest common factor number .

Step-1: Prime Factorization of 19536

Prime factors of 19536 are 2, 3, 11, 37. Prime factorization of 19536 in exponential form is:

19536 = 2⁴ × 3¹ × 11¹ × 37¹

Step-2: Prime Factorization of 19542

Prime factors of 19542 are 2, 3, 3257. Prime factorization of 19542 in exponential form is:

19542 = 2¹ × 3¹ × 3257¹

Step-3: Factors of 19536

List of positive integer factors of 19536 that divides 19536 without a remainder.

1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 24, 33, 37, 44, 48, 66, 74, 88, 111, 132, 148, 176, 222, 264, 296, 407, 444, 528, 592, 814, 888, 1221, 1628, 1776, 2442, 3256, 4884, 6512, 9768

Step-4: Factors of 19542

List of positive integer factors of 19542 that divides 19536 without a remainder.

1, 2, 3, 6, 3257, 6514, 9771

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19536 and 19542. The biggest common factor number is the GCF number.
So the greatest common factor 19536 and 19542 is 6.

Also check out the Least Common Multiple of 19536 and 19542