What is the Greatest Common Factor of 21738 and 21749?

Greatest common factor (GCF) of 21738 and 21749 is 1.

GCF(21738,21749) = 1

We will now calculate the prime factors of 21738 and 21749, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21738 and 21749.

How to find the GCF of 21738 and 21749?

We will first find the prime factorization of 21738 and 21749. After we will calculate the factors of 21738 and 21749 and find the biggest common factor number .

Step-1: Prime Factorization of 21738

Prime factors of 21738 are 2, 3, 3623. Prime factorization of 21738 in exponential form is:

21738 = 2¹ × 3¹ × 3623¹

Step-2: Prime Factorization of 21749

Prime factors of 21749 are 7, 13, 239. Prime factorization of 21749 in exponential form is:

21749 = 7¹ × 13¹ × 239¹

Step-3: Factors of 21738

List of positive integer factors of 21738 that divides 21738 without a remainder.

1, 2, 3, 6, 3623, 7246, 10869

Step-4: Factors of 21749

List of positive integer factors of 21749 that divides 21738 without a remainder.

1, 7, 13, 91, 239, 1673, 3107

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21738 and 21749. The biggest common factor number is the GCF number.
So the greatest common factor 21738 and 21749 is 1.

Also check out the Least Common Multiple of 21738 and 21749