What is the Greatest Common Factor of 21758 and 21769?

Greatest common factor (GCF) of 21758 and 21769 is 11.

GCF(21758,21769) = 11

We will now calculate the prime factors of 21758 and 21769, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21758 and 21769.

How to find the GCF of 21758 and 21769?

We will first find the prime factorization of 21758 and 21769. After we will calculate the factors of 21758 and 21769 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 21769

Prime factors of 21769 are 11, 1979. Prime factorization of 21769 in exponential form is:

21769 = 11¹ × 1979¹

Step-3: Factors of 21758

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

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

Step-4: Factors of 21769

List of positive integer factors of 21769 that divides 21758 without a remainder.

1, 11, 1979

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21758 and 21769. The biggest common factor number is the GCF number.
So the greatest common factor 21758 and 21769 is 11.

Also check out the Least Common Multiple of 21758 and 21769