What is the Greatest Common Factor of 16975 and 16982?

Greatest common factor (GCF) of 16975 and 16982 is 7.

GCF(16975,16982) = 7

We will now calculate the prime factors of 16975 and 16982, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 16975 and 16982.

How to find the GCF of 16975 and 16982?

We will first find the prime factorization of 16975 and 16982. After we will calculate the factors of 16975 and 16982 and find the biggest common factor number .

Step-1: Prime Factorization of 16975

Prime factors of 16975 are 5, 7, 97. Prime factorization of 16975 in exponential form is:

16975 = 5² × 7¹ × 97¹

Step-2: Prime Factorization of 16982

Prime factors of 16982 are 2, 7, 1213. Prime factorization of 16982 in exponential form is:

16982 = 2¹ × 7¹ × 1213¹

Step-3: Factors of 16975

List of positive integer factors of 16975 that divides 16975 without a remainder.

1, 5, 7, 25, 35, 97, 175, 485, 679, 2425, 3395

Step-4: Factors of 16982

List of positive integer factors of 16982 that divides 16975 without a remainder.

1, 2, 7, 14, 1213, 2426, 8491

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 16975 and 16982. The biggest common factor number is the GCF number.
So the greatest common factor 16975 and 16982 is 7.

Also check out the Least Common Multiple of 16975 and 16982