What is the Greatest Common Factor of 29700 and 29712?

Greatest common factor (GCF) of 29700 and 29712 is 12.

GCF(29700,29712) = 12

We will now calculate the prime factors of 29700 and 29712, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29700 and 29712.

How to find the GCF of 29700 and 29712?

We will first find the prime factorization of 29700 and 29712. After we will calculate the factors of 29700 and 29712 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 29712

Prime factors of 29712 are 2, 3, 619. Prime factorization of 29712 in exponential form is:

29712 = 2⁴ × 3¹ × 619¹

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 29712

List of positive integer factors of 29712 that divides 29700 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 619, 1238, 1857, 2476, 3714, 4952, 7428, 9904, 14856

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 29700 and 29712. The biggest common factor number is the GCF number.
So the greatest common factor 29700 and 29712 is 12.

Also check out the Least Common Multiple of 29700 and 29712