What is the Greatest Common Factor of 21384 and 21400?

Greatest common factor (GCF) of 21384 and 21400 is 8.

GCF(21384,21400) = 8

We will now calculate the prime factors of 21384 and 21400, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21384 and 21400.

How to find the GCF of 21384 and 21400?

We will first find the prime factorization of 21384 and 21400. After we will calculate the factors of 21384 and 21400 and find the biggest common factor number .

Step-1: Prime Factorization of 21384

Prime factors of 21384 are 2, 3, 11. Prime factorization of 21384 in exponential form is:

21384 = 2³ × 3⁵ × 11¹

Step-2: Prime Factorization of 21400

Prime factors of 21400 are 2, 5, 107. Prime factorization of 21400 in exponential form is:

21400 = 2³ × 5² × 107¹

Step-3: Factors of 21384

List of positive integer factors of 21384 that divides 21384 without a remainder.

1, 2, 3, 4, 6, 8, 9, 11, 12, 18, 22, 24, 27, 33, 36, 44, 54, 66, 72, 81, 88, 99, 108, 132, 162, 198, 216, 243, 264, 297, 324, 396, 486, 594, 648, 792, 891, 972, 1188, 1782, 1944, 2376, 2673, 3564, 5346, 7128, 10692

Step-4: Factors of 21400

List of positive integer factors of 21400 that divides 21384 without a remainder.

1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 107, 200, 214, 428, 535, 856, 1070, 2140, 2675, 4280, 5350, 10700

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21384 and 21400. The biggest common factor number is the GCF number.
So the greatest common factor 21384 and 21400 is 8.

Also check out the Least Common Multiple of 21384 and 21400