What is the Greatest Common Factor of 20972 and 20982?

Greatest common factor (GCF) of 20972 and 20982 is 2.

GCF(20972,20982) = 2

We will now calculate the prime factors of 20972 and 20982, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 20972 and 20982.

How to find the GCF of 20972 and 20982?

We will first find the prime factorization of 20972 and 20982. After we will calculate the factors of 20972 and 20982 and find the biggest common factor number .

Step-1: Prime Factorization of 20972

Prime factors of 20972 are 2, 7, 107. Prime factorization of 20972 in exponential form is:

20972 = 2² × 7² × 107¹

Step-2: Prime Factorization of 20982

Prime factors of 20982 are 2, 3, 13, 269. Prime factorization of 20982 in exponential form is:

20982 = 2¹ × 3¹ × 13¹ × 269¹

Step-3: Factors of 20972

List of positive integer factors of 20972 that divides 20972 without a remainder.

1, 2, 4, 7, 14, 28, 49, 98, 107, 196, 214, 428, 749, 1498, 2996, 5243, 10486

Step-4: Factors of 20982

List of positive integer factors of 20982 that divides 20972 without a remainder.

1, 2, 3, 6, 13, 26, 39, 78, 269, 538, 807, 1614, 3497, 6994, 10491

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 20972 and 20982. The biggest common factor number is the GCF number.
So the greatest common factor 20972 and 20982 is 2.

Also check out the Least Common Multiple of 20972 and 20982