What is the Greatest Common Factor of 9972 and 9982?

Greatest common factor (GCF) of 9972 and 9982 is 2.

GCF(9972,9982) = 2

We will now calculate the prime factors of 9972 and 9982, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 9972 and 9982.

How to find the GCF of 9972 and 9982?

We will first find the prime factorization of 9972 and 9982. After we will calculate the factors of 9972 and 9982 and find the biggest common factor number .

Step-1: Prime Factorization of 9972

Prime factors of 9972 are 2, 3, 277. Prime factorization of 9972 in exponential form is:

9972 = 2² × 3² × 277¹

Step-2: Prime Factorization of 9982

Prime factors of 9982 are 2, 7, 23, 31. Prime factorization of 9982 in exponential form is:

9982 = 2¹ × 7¹ × 23¹ × 31¹

Step-3: Factors of 9972

List of positive integer factors of 9972 that divides 9972 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 36, 277, 554, 831, 1108, 1662, 2493, 3324, 4986

Step-4: Factors of 9982

List of positive integer factors of 9982 that divides 9972 without a remainder.

1, 2, 7, 14, 23, 31, 46, 62, 161, 217, 322, 434, 713, 1426, 4991

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 9972 and 9982. The biggest common factor number is the GCF number.
So the greatest common factor 9972 and 9982 is 2.

Also check out the Least Common Multiple of 9972 and 9982