What is the Greatest Common Factor of 21754 and 21758?

Greatest common factor (GCF) of 21754 and 21758 is 2.

GCF(21754,21758) = 2

We will now calculate the prime factors of 21754 and 21758, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21754 and 21758.

How to find the GCF of 21754 and 21758?

We will first find the prime factorization of 21754 and 21758. After we will calculate the factors of 21754 and 21758 and find the biggest common factor number .

Step-1: 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-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 21754

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

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

Step-4: Factors of 21758

List of positive integer factors of 21758 that divides 21754 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 21754 and 21758. The biggest common factor number is the GCF number.
So the greatest common factor 21754 and 21758 is 2.

Also check out the Least Common Multiple of 21754 and 21758