What is the Greatest Common Factor of 34496 and 34510?

Greatest common factor (GCF) of 34496 and 34510 is 14.

GCF(34496,34510) = 14

We will now calculate the prime factors of 34496 and 34510, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34496 and 34510.

How to find the GCF of 34496 and 34510?

We will first find the prime factorization of 34496 and 34510. After we will calculate the factors of 34496 and 34510 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 34510

Prime factors of 34510 are 2, 5, 7, 17, 29. Prime factorization of 34510 in exponential form is:

34510 = 2¹ × 5¹ × 7¹ × 17¹ × 29¹

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 34510

List of positive integer factors of 34510 that divides 34496 without a remainder.

1, 2, 5, 7, 10, 14, 17, 29, 34, 35, 58, 70, 85, 119, 145, 170, 203, 238, 290, 406, 493, 595, 986, 1015, 1190, 2030, 2465, 3451, 4930, 6902, 17255

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34496 and 34510. The biggest common factor number is the GCF number.
So the greatest common factor 34496 and 34510 is 14.

Also check out the Least Common Multiple of 34496 and 34510