What is the Greatest Common Factor of 3456 and 3465?

Greatest common factor (GCF) of 3456 and 3465 is 9.

GCF(3456,3465) = 9

We will now calculate the prime factors of 3456 and 3465, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 3456 and 3465.

How to find the GCF of 3456 and 3465?

We will first find the prime factorization of 3456 and 3465. After we will calculate the factors of 3456 and 3465 and find the biggest common factor number .

Step-1: Prime Factorization of 3456

Prime factors of 3456 are 2, 3. Prime factorization of 3456 in exponential form is:

3456 = 2⁷ × 3³

Step-2: Prime Factorization of 3465

Prime factors of 3465 are 3, 5, 7, 11. Prime factorization of 3465 in exponential form is:

3465 = 3² × 5¹ × 7¹ × 11¹

Step-3: Factors of 3456

List of positive integer factors of 3456 that divides 3456 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 96, 108, 128, 144, 192, 216, 288, 384, 432, 576, 864, 1152, 1728

Step-4: Factors of 3465

List of positive integer factors of 3465 that divides 3456 without a remainder.

1, 3, 5, 7, 9, 11, 15, 21, 33, 35, 45, 55, 63, 77, 99, 105, 165, 231, 315, 385, 495, 693, 1155

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 3456 and 3465. The biggest common factor number is the GCF number.
So the greatest common factor 3456 and 3465 is 9.

Also check out the Least Common Multiple of 3456 and 3465