What is the Greatest Common Factor of 16905 and 16914?

Greatest common factor (GCF) of 16905 and 16914 is 3.

GCF(16905,16914) = 3

We will now calculate the prime factors of 16905 and 16914, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 16905 and 16914.

How to find the GCF of 16905 and 16914?

We will first find the prime factorization of 16905 and 16914. After we will calculate the factors of 16905 and 16914 and find the biggest common factor number .

Step-1: Prime Factorization of 16905

Prime factors of 16905 are 3, 5, 7, 23. Prime factorization of 16905 in exponential form is:

16905 = 3¹ × 5¹ × 7² × 23¹

Step-2: Prime Factorization of 16914

Prime factors of 16914 are 2, 3, 2819. Prime factorization of 16914 in exponential form is:

16914 = 2¹ × 3¹ × 2819¹

Step-3: Factors of 16905

List of positive integer factors of 16905 that divides 16905 without a remainder.

1, 3, 5, 7, 15, 21, 23, 35, 49, 69, 105, 115, 147, 161, 245, 345, 483, 735, 805, 1127, 2415, 3381, 5635

Step-4: Factors of 16914

List of positive integer factors of 16914 that divides 16905 without a remainder.

1, 2, 3, 6, 2819, 5638, 8457

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 16905 and 16914. The biggest common factor number is the GCF number.
So the greatest common factor 16905 and 16914 is 3.

Also check out the Least Common Multiple of 16905 and 16914