What is the Greatest Common Factor of 21752 and 21758?

Greatest common factor (GCF) of 21752 and 21758 is 2.

GCF(21752,21758) = 2

We will now calculate the prime factors of 21752 and 21758, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21752 and 21758.

How to find the GCF of 21752 and 21758?

We will first find the prime factorization of 21752 and 21758. After we will calculate the factors of 21752 and 21758 and find the biggest common factor number .

Step-1: Prime Factorization of 21752

Prime factors of 21752 are 2, 2719. Prime factorization of 21752 in exponential form is:

21752 = 2³ × 2719¹

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 21752

List of positive integer factors of 21752 that divides 21752 without a remainder.

1, 2, 4, 8, 2719, 5438, 10876

Step-4: Factors of 21758

List of positive integer factors of 21758 that divides 21752 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 21752 and 21758. The biggest common factor number is the GCF number.
So the greatest common factor 21752 and 21758 is 2.

Also check out the Least Common Multiple of 21752 and 21758