What is the Greatest Common Factor of 1990 and 1998?

Greatest common factor (GCF) of 1990 and 1998 is 2.

GCF(1990,1998) = 2

We will now calculate the prime factors of 1990 and 1998, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1990 and 1998.

How to find the GCF of 1990 and 1998?

We will first find the prime factorization of 1990 and 1998. After we will calculate the factors of 1990 and 1998 and find the biggest common factor number .

Step-1: Prime Factorization of 1990

Prime factors of 1990 are 2, 5, 199. Prime factorization of 1990 in exponential form is:

1990 = 2¹ × 5¹ × 199¹

Step-2: Prime Factorization of 1998

Prime factors of 1998 are 2, 3, 37. Prime factorization of 1998 in exponential form is:

1998 = 2¹ × 3³ × 37¹

Step-3: Factors of 1990

List of positive integer factors of 1990 that divides 1990 without a remainder.

1, 2, 5, 10, 199, 398, 995

Step-4: Factors of 1998

List of positive integer factors of 1998 that divides 1990 without a remainder.

1, 2, 3, 6, 9, 18, 27, 37, 54, 74, 111, 222, 333, 666, 999

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1990 and 1998. The biggest common factor number is the GCF number.
So the greatest common factor 1990 and 1998 is 2.

Also check out the Least Common Multiple of 1990 and 1998