What is the Greatest Common Factor of 3405 and 3414?

Greatest common factor (GCF) of 3405 and 3414 is 3.

GCF(3405,3414) = 3

We will now calculate the prime factors of 3405 and 3414, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 3405 and 3414.

How to find the GCF of 3405 and 3414?

We will first find the prime factorization of 3405 and 3414. After we will calculate the factors of 3405 and 3414 and find the biggest common factor number .

Step-1: Prime Factorization of 3405

Prime factors of 3405 are 3, 5, 227. Prime factorization of 3405 in exponential form is:

3405 = 3¹ × 5¹ × 227¹

Step-2: Prime Factorization of 3414

Prime factors of 3414 are 2, 3, 569. Prime factorization of 3414 in exponential form is:

3414 = 2¹ × 3¹ × 569¹

Step-3: Factors of 3405

List of positive integer factors of 3405 that divides 3405 without a remainder.

1, 3, 5, 15, 227, 681, 1135

Step-4: Factors of 3414

List of positive integer factors of 3414 that divides 3405 without a remainder.

1, 2, 3, 6, 569, 1138, 1707

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 3405 and 3414. The biggest common factor number is the GCF number.
So the greatest common factor 3405 and 3414 is 3.

Also check out the Least Common Multiple of 3405 and 3414