What is the Greatest Common Factor of 21738 and 21754?

Greatest common factor (GCF) of 21738 and 21754 is 2.

GCF(21738,21754) = 2

We will now calculate the prime factors of 21738 and 21754, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21738 and 21754.

How to find the GCF of 21738 and 21754?

We will first find the prime factorization of 21738 and 21754. After we will calculate the factors of 21738 and 21754 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 21754

Prime factors of 21754 are 2, 73, 149. Prime factorization of 21754 in exponential form is:

21754 = 2¹ × 73¹ × 149¹

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 21754

List of positive integer factors of 21754 that divides 21738 without a remainder.

1, 2, 73, 146, 149, 298, 10877

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21738 and 21754. The biggest common factor number is the GCF number.
So the greatest common factor 21738 and 21754 is 2.

Also check out the Least Common Multiple of 21738 and 21754