What is the Greatest Common Factor of 21705 and 21712?

Greatest common factor (GCF) of 21705 and 21712 is 1.

GCF(21705,21712) = 1

We will now calculate the prime factors of 21705 and 21712, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21705 and 21712.

How to find the GCF of 21705 and 21712?

We will first find the prime factorization of 21705 and 21712. After we will calculate the factors of 21705 and 21712 and find the biggest common factor number .

Step-1: Prime Factorization of 21705

Prime factors of 21705 are 3, 5, 1447. Prime factorization of 21705 in exponential form is:

21705 = 3¹ × 5¹ × 1447¹

Step-2: Prime Factorization of 21712

Prime factors of 21712 are 2, 23, 59. Prime factorization of 21712 in exponential form is:

21712 = 2⁴ × 23¹ × 59¹

Step-3: Factors of 21705

List of positive integer factors of 21705 that divides 21705 without a remainder.

1, 3, 5, 15, 1447, 4341, 7235

Step-4: Factors of 21712

List of positive integer factors of 21712 that divides 21705 without a remainder.

1, 2, 4, 8, 16, 23, 46, 59, 92, 118, 184, 236, 368, 472, 944, 1357, 2714, 5428, 10856

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21705 and 21712. The biggest common factor number is the GCF number.
So the greatest common factor 21705 and 21712 is 1.

Also check out the Least Common Multiple of 21705 and 21712