What is the Greatest Common Factor of 14800 and 14820?

Greatest common factor (GCF) of 14800 and 14820 is 20.

GCF(14800,14820) = 20

We will now calculate the prime factors of 14800 and 14820, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14800 and 14820.

How to find the GCF of 14800 and 14820?

We will first find the prime factorization of 14800 and 14820. After we will calculate the factors of 14800 and 14820 and find the biggest common factor number .

Step-1: Prime Factorization of 14800

Prime factors of 14800 are 2, 5, 37. Prime factorization of 14800 in exponential form is:

14800 = 2⁴ × 5² × 37¹

Step-2: Prime Factorization of 14820

Prime factors of 14820 are 2, 3, 5, 13, 19. Prime factorization of 14820 in exponential form is:

14820 = 2² × 3¹ × 5¹ × 13¹ × 19¹

Step-3: Factors of 14800

List of positive integer factors of 14800 that divides 14800 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 37, 40, 50, 74, 80, 100, 148, 185, 200, 296, 370, 400, 592, 740, 925, 1480, 1850, 2960, 3700, 7400

Step-4: Factors of 14820

List of positive integer factors of 14820 that divides 14800 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 19, 20, 26, 30, 38, 39, 52, 57, 60, 65, 76, 78, 95, 114, 130, 156, 190, 195, 228, 247, 260, 285, 380, 390, 494, 570, 741, 780, 988, 1140, 1235, 1482, 2470, 2964, 3705, 4940, 7410

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14800 and 14820. The biggest common factor number is the GCF number.
So the greatest common factor 14800 and 14820 is 20.

Also check out the Least Common Multiple of 14800 and 14820