What is the Greatest Common Factor of 21872 and 21890?

Greatest common factor (GCF) of 21872 and 21890 is 2.

GCF(21872,21890) = 2

We will now calculate the prime factors of 21872 and 21890, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21872 and 21890.

How to find the GCF of 21872 and 21890?

We will first find the prime factorization of 21872 and 21890. After we will calculate the factors of 21872 and 21890 and find the biggest common factor number .

Step-1: Prime Factorization of 21872

Prime factors of 21872 are 2, 1367. Prime factorization of 21872 in exponential form is:

21872 = 2⁴ × 1367¹

Step-2: Prime Factorization of 21890

Prime factors of 21890 are 2, 5, 11, 199. Prime factorization of 21890 in exponential form is:

21890 = 2¹ × 5¹ × 11¹ × 199¹

Step-3: Factors of 21872

List of positive integer factors of 21872 that divides 21872 without a remainder.

1, 2, 4, 8, 16, 1367, 2734, 5468, 10936

Step-4: Factors of 21890

List of positive integer factors of 21890 that divides 21872 without a remainder.

1, 2, 5, 10, 11, 22, 55, 110, 199, 398, 995, 1990, 2189, 4378, 10945

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21872 and 21890. The biggest common factor number is the GCF number.
So the greatest common factor 21872 and 21890 is 2.

Also check out the Least Common Multiple of 21872 and 21890