What is the Greatest Common Factor of 34496 and 34509?

Greatest common factor (GCF) of 34496 and 34509 is 1.

GCF(34496,34509) = 1

We will now calculate the prime factors of 34496 and 34509, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34496 and 34509.

How to find the GCF of 34496 and 34509?

We will first find the prime factorization of 34496 and 34509. After we will calculate the factors of 34496 and 34509 and find the biggest common factor number .

Step-1: Prime Factorization of 34496

Prime factors of 34496 are 2, 7, 11. Prime factorization of 34496 in exponential form is:

34496 = 2⁶ × 7² × 11¹

Step-2: Prime Factorization of 34509

Prime factors of 34509 are 3, 11503. Prime factorization of 34509 in exponential form is:

34509 = 3¹ × 11503¹

Step-3: Factors of 34496

List of positive integer factors of 34496 that divides 34496 without a remainder.

1, 2, 4, 7, 8, 11, 14, 16, 22, 28, 32, 44, 49, 56, 64, 77, 88, 98, 112, 154, 176, 196, 224, 308, 352, 392, 448, 539, 616, 704, 784, 1078, 1232, 1568, 2156, 2464, 3136, 4312, 4928, 8624, 17248

Step-4: Factors of 34509

List of positive integer factors of 34509 that divides 34496 without a remainder.

1, 3, 11503

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34496 and 34509. The biggest common factor number is the GCF number.
So the greatest common factor 34496 and 34509 is 1.

Also check out the Least Common Multiple of 34496 and 34509