What is the Greatest Common Factor of 21364 and 21384?

Greatest common factor (GCF) of 21364 and 21384 is 4.

GCF(21364,21384) = 4

We will now calculate the prime factors of 21364 and 21384, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21364 and 21384.

How to find the GCF of 21364 and 21384?

We will first find the prime factorization of 21364 and 21384. After we will calculate the factors of 21364 and 21384 and find the biggest common factor number .

Step-1: Prime Factorization of 21364

Prime factors of 21364 are 2, 7, 109. Prime factorization of 21364 in exponential form is:

21364 = 2² × 7² × 109¹

Step-2: 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-3: Factors of 21364

List of positive integer factors of 21364 that divides 21364 without a remainder.

1, 2, 4, 7, 14, 28, 49, 98, 109, 196, 218, 436, 763, 1526, 3052, 5341, 10682

Step-4: Factors of 21384

List of positive integer factors of 21384 that divides 21364 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21364 and 21384. The biggest common factor number is the GCF number.
So the greatest common factor 21364 and 21384 is 4.

Also check out the Least Common Multiple of 21364 and 21384