What is the Greatest Common Factor of 34800 and 34804?

Greatest common factor (GCF) of 34800 and 34804 is 4.

GCF(34800,34804) = 4

We will now calculate the prime factors of 34800 and 34804, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34800 and 34804.

How to find the GCF of 34800 and 34804?

We will first find the prime factorization of 34800 and 34804. After we will calculate the factors of 34800 and 34804 and find the biggest common factor number .

Step-1: Prime Factorization of 34800

Prime factors of 34800 are 2, 3, 5, 29. Prime factorization of 34800 in exponential form is:

34800 = 2⁴ × 3¹ × 5² × 29¹

Step-2: Prime Factorization of 34804

Prime factors of 34804 are 2, 7, 11, 113. Prime factorization of 34804 in exponential form is:

34804 = 2² × 7¹ × 11¹ × 113¹

Step-3: Factors of 34800

List of positive integer factors of 34800 that divides 34800 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 29, 30, 40, 48, 50, 58, 60, 75, 80, 87, 100, 116, 120, 145, 150, 174, 200, 232, 240, 290, 300, 348, 400, 435, 464, 580, 600, 696, 725, 870, 1160, 1200, 1392, 1450, 1740, 2175, 2320, 2900, 3480, 4350, 5800, 6960, 8700, 11600, 17400

Step-4: Factors of 34804

List of positive integer factors of 34804 that divides 34800 without a remainder.

1, 2, 4, 7, 11, 14, 22, 28, 44, 77, 113, 154, 226, 308, 452, 791, 1243, 1582, 2486, 3164, 4972, 8701, 17402

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34800 and 34804. The biggest common factor number is the GCF number.
So the greatest common factor 34800 and 34804 is 4.

Also check out the Least Common Multiple of 34800 and 34804