What is the Greatest Common Factor of 32814 and 32832?

Greatest common factor (GCF) of 32814 and 32832 is 18.

GCF(32814,32832) = 18

We will now calculate the prime factors of 32814 and 32832, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 32814 and 32832.

How to find the GCF of 32814 and 32832?

We will first find the prime factorization of 32814 and 32832. After we will calculate the factors of 32814 and 32832 and find the biggest common factor number .

Step-1: Prime Factorization of 32814

Prime factors of 32814 are 2, 3, 1823. Prime factorization of 32814 in exponential form is:

32814 = 2¹ × 3² × 1823¹

Step-2: Prime Factorization of 32832

Prime factors of 32832 are 2, 3, 19. Prime factorization of 32832 in exponential form is:

32832 = 2⁶ × 3³ × 19¹

Step-3: Factors of 32814

List of positive integer factors of 32814 that divides 32814 without a remainder.

1, 2, 3, 6, 9, 18, 1823, 3646, 5469, 10938, 16407

Step-4: Factors of 32832

List of positive integer factors of 32832 that divides 32814 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 19, 24, 27, 32, 36, 38, 48, 54, 57, 64, 72, 76, 96, 108, 114, 144, 152, 171, 192, 216, 228, 288, 304, 342, 432, 456, 513, 576, 608, 684, 864, 912, 1026, 1216, 1368, 1728, 1824, 2052, 2736, 3648, 4104, 5472, 8208, 10944, 16416

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 32814 and 32832. The biggest common factor number is the GCF number.
So the greatest common factor 32814 and 32832 is 18.

Also check out the Least Common Multiple of 32814 and 32832