What is the Greatest Common Factor of 21738 and 21758?

Greatest common factor (GCF) of 21738 and 21758 is 2.

GCF(21738,21758) = 2

We will now calculate the prime factors of 21738 and 21758, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21738 and 21758.

How to find the GCF of 21738 and 21758?

We will first find the prime factorization of 21738 and 21758. After we will calculate the factors of 21738 and 21758 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 21758

Prime factors of 21758 are 2, 11, 23, 43. Prime factorization of 21758 in exponential form is:

21758 = 2¹ × 11¹ × 23¹ × 43¹

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 21758

List of positive integer factors of 21758 that divides 21738 without a remainder.

1, 2, 11, 22, 23, 43, 46, 86, 253, 473, 506, 946, 989, 1978, 10879

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21738 and 21758. The biggest common factor number is the GCF number.
So the greatest common factor 21738 and 21758 is 2.

Also check out the Least Common Multiple of 21738 and 21758