What is the Greatest Common Factor of 19536 and 19552?

Greatest common factor (GCF) of 19536 and 19552 is 16.

GCF(19536,19552) = 16

We will now calculate the prime factors of 19536 and 19552, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19536 and 19552.

How to find the GCF of 19536 and 19552?

We will first find the prime factorization of 19536 and 19552. After we will calculate the factors of 19536 and 19552 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 19552

Prime factors of 19552 are 2, 13, 47. Prime factorization of 19552 in exponential form is:

19552 = 2⁵ × 13¹ × 47¹

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 19552

List of positive integer factors of 19552 that divides 19536 without a remainder.

1, 2, 4, 8, 13, 16, 26, 32, 47, 52, 94, 104, 188, 208, 376, 416, 611, 752, 1222, 1504, 2444, 4888, 9776

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19536 and 19552. The biggest common factor number is the GCF number.
So the greatest common factor 19536 and 19552 is 16.

Also check out the Least Common Multiple of 19536 and 19552