What is the Greatest Common Factor of 20991 and 21009?

Greatest common factor (GCF) of 20991 and 21009 is 3.

GCF(20991,21009) = 3

We will now calculate the prime factors of 20991 and 21009, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 20991 and 21009.

How to find the GCF of 20991 and 21009?

We will first find the prime factorization of 20991 and 21009. After we will calculate the factors of 20991 and 21009 and find the biggest common factor number .

Step-1: Prime Factorization of 20991

Prime factors of 20991 are 3, 6997. Prime factorization of 20991 in exponential form is:

20991 = 3¹ × 6997¹

Step-2: Prime Factorization of 21009

Prime factors of 21009 are 3, 47, 149. Prime factorization of 21009 in exponential form is:

21009 = 3¹ × 47¹ × 149¹

Step-3: Factors of 20991

List of positive integer factors of 20991 that divides 20991 without a remainder.

1, 3, 6997

Step-4: Factors of 21009

List of positive integer factors of 21009 that divides 20991 without a remainder.

1, 3, 47, 141, 149, 447, 7003

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 20991 and 21009. The biggest common factor number is the GCF number.
So the greatest common factor 20991 and 21009 is 3.

Also check out the Least Common Multiple of 20991 and 21009