What is the Greatest Common Factor of 29685 and 29700?

Greatest common factor (GCF) of 29685 and 29700 is 15.

GCF(29685,29700) = 15

We will now calculate the prime factors of 29685 and 29700, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29685 and 29700.

How to find the GCF of 29685 and 29700?

We will first find the prime factorization of 29685 and 29700. After we will calculate the factors of 29685 and 29700 and find the biggest common factor number .

Step-1: Prime Factorization of 29685

Prime factors of 29685 are 3, 5, 1979. Prime factorization of 29685 in exponential form is:

29685 = 3¹ × 5¹ × 1979¹

Step-2: 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-3: Factors of 29685

List of positive integer factors of 29685 that divides 29685 without a remainder.

1, 3, 5, 15, 1979, 5937, 9895

Step-4: Factors of 29700

List of positive integer factors of 29700 that divides 29685 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 29685 and 29700. The biggest common factor number is the GCF number.
So the greatest common factor 29685 and 29700 is 15.

Also check out the Least Common Multiple of 29685 and 29700