What is the Greatest Common Factor of 34896 and 34914?

Greatest common factor (GCF) of 34896 and 34914 is 6.

GCF(34896,34914) = 6

We will now calculate the prime factors of 34896 and 34914, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34896 and 34914.

How to find the GCF of 34896 and 34914?

We will first find the prime factorization of 34896 and 34914. After we will calculate the factors of 34896 and 34914 and find the biggest common factor number .

Step-1: Prime Factorization of 34896

Prime factors of 34896 are 2, 3, 727. Prime factorization of 34896 in exponential form is:

34896 = 2⁴ × 3¹ × 727¹

Step-2: Prime Factorization of 34914

Prime factors of 34914 are 2, 3, 11, 23. Prime factorization of 34914 in exponential form is:

34914 = 2¹ × 3¹ × 11¹ × 23²

Step-3: Factors of 34896

List of positive integer factors of 34896 that divides 34896 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 727, 1454, 2181, 2908, 4362, 5816, 8724, 11632, 17448

Step-4: Factors of 34914

List of positive integer factors of 34914 that divides 34896 without a remainder.

1, 2, 3, 6, 11, 22, 23, 33, 46, 66, 69, 138, 253, 506, 529, 759, 1058, 1518, 1587, 3174, 5819, 11638, 17457

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34896 and 34914. The biggest common factor number is the GCF number.
So the greatest common factor 34896 and 34914 is 6.

Also check out the Least Common Multiple of 34896 and 34914