What is the Greatest Common Factor of 29688 and 29700?

Greatest common factor (GCF) of 29688 and 29700 is 12.

GCF(29688,29700) = 12

We will now calculate the prime factors of 29688 and 29700, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29688 and 29700.

How to find the GCF of 29688 and 29700?

We will first find the prime factorization of 29688 and 29700. After we will calculate the factors of 29688 and 29700 and find the biggest common factor number .

Step-1: Prime Factorization of 29688

Prime factors of 29688 are 2, 3, 1237. Prime factorization of 29688 in exponential form is:

29688 = 2³ × 3¹ × 1237¹

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 29688

List of positive integer factors of 29688 that divides 29688 without a remainder.

1, 2, 3, 4, 6, 8, 12, 24, 1237, 2474, 3711, 4948, 7422, 9896, 14844

Step-4: Factors of 29700

List of positive integer factors of 29700 that divides 29688 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 29688 and 29700. The biggest common factor number is the GCF number.
So the greatest common factor 29688 and 29700 is 12.

Also check out the Least Common Multiple of 29688 and 29700