What is the Greatest Common Factor of 29700 and 29715?

Greatest common factor (GCF) of 29700 and 29715 is 15.

GCF(29700,29715) = 15

We will now calculate the prime factors of 29700 and 29715, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29700 and 29715.

How to find the GCF of 29700 and 29715?

We will first find the prime factorization of 29700 and 29715. After we will calculate the factors of 29700 and 29715 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 29715

Prime factors of 29715 are 3, 5, 7, 283. Prime factorization of 29715 in exponential form is:

29715 = 3¹ × 5¹ × 7¹ × 283¹

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 29715

List of positive integer factors of 29715 that divides 29700 without a remainder.

1, 3, 5, 7, 15, 21, 35, 105, 283, 849, 1415, 1981, 4245, 5943, 9905

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 29700 and 29715. The biggest common factor number is the GCF number.
So the greatest common factor 29700 and 29715 is 15.

Also check out the Least Common Multiple of 29700 and 29715