What is the Greatest Common Factor of 19525 and 19536?

Greatest common factor (GCF) of 19525 and 19536 is 11.

GCF(19525,19536) = 11

We will now calculate the prime factors of 19525 and 19536, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19525 and 19536.

How to find the GCF of 19525 and 19536?

We will first find the prime factorization of 19525 and 19536. After we will calculate the factors of 19525 and 19536 and find the biggest common factor number .

Step-1: Prime Factorization of 19525

Prime factors of 19525 are 5, 11, 71. Prime factorization of 19525 in exponential form is:

19525 = 5² × 11¹ × 71¹

Step-2: 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-3: Factors of 19525

List of positive integer factors of 19525 that divides 19525 without a remainder.

1, 5, 11, 25, 55, 71, 275, 355, 781, 1775, 3905

Step-4: Factors of 19536

List of positive integer factors of 19536 that divides 19525 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19525 and 19536. The biggest common factor number is the GCF number.
So the greatest common factor 19525 and 19536 is 11.

Also check out the Least Common Multiple of 19525 and 19536