What is the Greatest Common Factor of 16409 and 16416?

Greatest common factor (GCF) of 16409 and 16416 is 1.

GCF(16409,16416) = 1

We will now calculate the prime factors of 16409 and 16416, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 16409 and 16416.

How to find the GCF of 16409 and 16416?

We will first find the prime factorization of 16409 and 16416. After we will calculate the factors of 16409 and 16416 and find the biggest common factor number .

Step-1: Prime Factorization of 16409

Prime factors of 16409 are 61, 269. Prime factorization of 16409 in exponential form is:

16409 = 61¹ × 269¹

Step-2: Prime Factorization of 16416

Prime factors of 16416 are 2, 3, 19. Prime factorization of 16416 in exponential form is:

16416 = 2⁵ × 3³ × 19¹

Step-3: Factors of 16409

List of positive integer factors of 16409 that divides 16409 without a remainder.

1, 61, 269

Step-4: Factors of 16416

List of positive integer factors of 16416 that divides 16409 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 16409 and 16416. The biggest common factor number is the GCF number.
So the greatest common factor 16409 and 16416 is 1.

Also check out the Least Common Multiple of 16409 and 16416