What is the Greatest Common Factor of 34496 and 34512?

Greatest common factor (GCF) of 34496 and 34512 is 16.

GCF(34496,34512) = 16

We will now calculate the prime factors of 34496 and 34512, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34496 and 34512.

How to find the GCF of 34496 and 34512?

We will first find the prime factorization of 34496 and 34512. After we will calculate the factors of 34496 and 34512 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 34512

Prime factors of 34512 are 2, 3, 719. Prime factorization of 34512 in exponential form is:

34512 = 2⁴ × 3¹ × 719¹

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 34512

List of positive integer factors of 34512 that divides 34496 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 719, 1438, 2157, 2876, 4314, 5752, 8628, 11504, 17256

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34496 and 34512. The biggest common factor number is the GCF number.
So the greatest common factor 34496 and 34512 is 16.

Also check out the Least Common Multiple of 34496 and 34512