What is the Greatest Common Factor of 34800 and 34820?

Greatest common factor (GCF) of 34800 and 34820 is 20.

GCF(34800,34820) = 20

We will now calculate the prime factors of 34800 and 34820, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34800 and 34820.

How to find the GCF of 34800 and 34820?

We will first find the prime factorization of 34800 and 34820. After we will calculate the factors of 34800 and 34820 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 34820

Prime factors of 34820 are 2, 5, 1741. Prime factorization of 34820 in exponential form is:

34820 = 2² × 5¹ × 1741¹

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 34820

List of positive integer factors of 34820 that divides 34800 without a remainder.

1, 2, 4, 5, 10, 20, 1741, 3482, 6964, 8705, 17410

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34800 and 34820. The biggest common factor number is the GCF number.
So the greatest common factor 34800 and 34820 is 20.

Also check out the Least Common Multiple of 34800 and 34820