What is the Greatest Common Factor of 34900 and 34914?

Greatest common factor (GCF) of 34900 and 34914 is 2.

GCF(34900,34914) = 2

We will now calculate the prime factors of 34900 and 34914, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34900 and 34914.

How to find the GCF of 34900 and 34914?

We will first find the prime factorization of 34900 and 34914. After we will calculate the factors of 34900 and 34914 and find the biggest common factor number .

Step-1: Prime Factorization of 34900

Prime factors of 34900 are 2, 5, 349. Prime factorization of 34900 in exponential form is:

34900 = 2² × 5² × 349¹

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 34900

List of positive integer factors of 34900 that divides 34900 without a remainder.

1, 2, 4, 5, 10, 20, 25, 50, 100, 349, 698, 1396, 1745, 3490, 6980, 8725, 17450

Step-4: Factors of 34914

List of positive integer factors of 34914 that divides 34900 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 34900 and 34914. The biggest common factor number is the GCF number.
So the greatest common factor 34900 and 34914 is 2.

Also check out the Least Common Multiple of 34900 and 34914