What is the Greatest Common Factor of 29700 and 29705?

Greatest common factor (GCF) of 29700 and 29705 is 5.

GCF(29700,29705) = 5

We will now calculate the prime factors of 29700 and 29705, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29700 and 29705.

How to find the GCF of 29700 and 29705?

We will first find the prime factorization of 29700 and 29705. After we will calculate the factors of 29700 and 29705 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 29705

Prime factors of 29705 are 5, 13, 457. Prime factorization of 29705 in exponential form is:

29705 = 5¹ × 13¹ × 457¹

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 29705

List of positive integer factors of 29705 that divides 29700 without a remainder.

1, 5, 13, 65, 457, 2285, 5941

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 29700 and 29705. The biggest common factor number is the GCF number.
So the greatest common factor 29700 and 29705 is 5.

Also check out the Least Common Multiple of 29700 and 29705