What is the Greatest Common Factor of 20971 and 20988?

Greatest common factor (GCF) of 20971 and 20988 is 1.

GCF(20971,20988) = 1

We will now calculate the prime factors of 20971 and 20988, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 20971 and 20988.

How to find the GCF of 20971 and 20988?

We will first find the prime factorization of 20971 and 20988. After we will calculate the factors of 20971 and 20988 and find the biggest common factor number .

Step-1: Prime Factorization of 20971

Prime factors of 20971 are 67, 313. Prime factorization of 20971 in exponential form is:

20971 = 67¹ × 313¹

Step-2: Prime Factorization of 20988

Prime factors of 20988 are 2, 3, 11, 53. Prime factorization of 20988 in exponential form is:

20988 = 2² × 3² × 11¹ × 53¹

Step-3: Factors of 20971

List of positive integer factors of 20971 that divides 20971 without a remainder.

1, 67, 313

Step-4: Factors of 20988

List of positive integer factors of 20988 that divides 20971 without a remainder.

1, 2, 3, 4, 6, 9, 11, 12, 18, 22, 33, 36, 44, 53, 66, 99, 106, 132, 159, 198, 212, 318, 396, 477, 583, 636, 954, 1166, 1749, 1908, 2332, 3498, 5247, 6996, 10494

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 20971 and 20988. The biggest common factor number is the GCF number.
So the greatest common factor 20971 and 20988 is 1.

Also check out the Least Common Multiple of 20971 and 20988