What is the Greatest Common Factor of 21527 and 21538?

Greatest common factor (GCF) of 21527 and 21538 is 11.

GCF(21527,21538) = 11

We will now calculate the prime factors of 21527 and 21538, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21527 and 21538.

How to find the GCF of 21527 and 21538?

We will first find the prime factorization of 21527 and 21538. After we will calculate the factors of 21527 and 21538 and find the biggest common factor number .

Step-1: Prime Factorization of 21527

Prime factors of 21527 are 11, 19, 103. Prime factorization of 21527 in exponential form is:

21527 = 11¹ × 19¹ × 103¹

Step-2: Prime Factorization of 21538

Prime factors of 21538 are 2, 11, 89. Prime factorization of 21538 in exponential form is:

21538 = 2¹ × 11² × 89¹

Step-3: Factors of 21527

List of positive integer factors of 21527 that divides 21527 without a remainder.

1, 11, 19, 103, 209, 1133, 1957

Step-4: Factors of 21538

List of positive integer factors of 21538 that divides 21527 without a remainder.

1, 2, 11, 22, 89, 121, 178, 242, 979, 1958, 10769

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21527 and 21538. The biggest common factor number is the GCF number.
So the greatest common factor 21527 and 21538 is 11.

Also check out the Least Common Multiple of 21527 and 21538