What is the Greatest Common Factor of 29700 and 29709?

Greatest common factor (GCF) of 29700 and 29709 is 9.

GCF(29700,29709) = 9

We will now calculate the prime factors of 29700 and 29709, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29700 and 29709.

How to find the GCF of 29700 and 29709?

We will first find the prime factorization of 29700 and 29709. After we will calculate the factors of 29700 and 29709 and find the biggest common factor number .

Step-1: Prime Factorization of 29700

Prime factors of 29700 are 2, 3, 5, 11. Prime factorization of 29700 in exponential form is:

29700 = 2² × 3³ × 5² × 11¹

Step-2: Prime Factorization of 29709

Prime factors of 29709 are 3, 3301. Prime factorization of 29709 in exponential form is:

29709 = 3² × 3301¹

Step-3: Factors of 29700

List of positive integer factors of 29700 that divides 29700 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 15, 18, 20, 22, 25, 27, 30, 33, 36, 44, 45, 50, 54, 55, 60, 66, 75, 90, 99, 100, 108, 110, 132, 135, 150, 165, 180, 198, 220, 225, 270, 275, 297, 300, 330, 396, 450, 495, 540, 550, 594, 660, 675, 825, 900, 990, 1100, 1188, 1350, 1485, 1650, 1980, 2475, 2700, 2970, 3300, 4950, 5940, 7425, 9900, 14850

Step-4: Factors of 29709

List of positive integer factors of 29709 that divides 29700 without a remainder.

1, 3, 9, 3301, 9903

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 29700 and 29709. The biggest common factor number is the GCF number.
So the greatest common factor 29700 and 29709 is 9.

Also check out the Least Common Multiple of 29700 and 29709