What is the Greatest Common Factor of 28380 and 28400?

Greatest common factor (GCF) of 28380 and 28400 is 20.

GCF(28380,28400) = 20

We will now calculate the prime factors of 28380 and 28400, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 28380 and 28400.

How to find the GCF of 28380 and 28400?

We will first find the prime factorization of 28380 and 28400. After we will calculate the factors of 28380 and 28400 and find the biggest common factor number .

Step-1: Prime Factorization of 28380

Prime factors of 28380 are 2, 3, 5, 11, 43. Prime factorization of 28380 in exponential form is:

28380 = 2² × 3¹ × 5¹ × 11¹ × 43¹

Step-2: Prime Factorization of 28400

Prime factors of 28400 are 2, 5, 71. Prime factorization of 28400 in exponential form is:

28400 = 2⁴ × 5² × 71¹

Step-3: Factors of 28380

List of positive integer factors of 28380 that divides 28380 without a remainder.

1, 2, 3, 4, 5, 6, 10, 11, 12, 15, 20, 22, 30, 33, 43, 44, 55, 60, 66, 86, 110, 129, 132, 165, 172, 215, 220, 258, 330, 430, 473, 516, 645, 660, 860, 946, 1290, 1419, 1892, 2365, 2580, 2838, 4730, 5676, 7095, 9460, 14190

Step-4: Factors of 28400

List of positive integer factors of 28400 that divides 28380 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 71, 80, 100, 142, 200, 284, 355, 400, 568, 710, 1136, 1420, 1775, 2840, 3550, 5680, 7100, 14200

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 28380 and 28400. The biggest common factor number is the GCF number.
So the greatest common factor 28380 and 28400 is 20.

Also check out the Least Common Multiple of 28380 and 28400