What is the Greatest Common Factor of 1985 and 1995?

Greatest common factor (GCF) of 1985 and 1995 is 5.

GCF(1985,1995) = 5

We will now calculate the prime factors of 1985 and 1995, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1985 and 1995.

How to find the GCF of 1985 and 1995?

We will first find the prime factorization of 1985 and 1995. After we will calculate the factors of 1985 and 1995 and find the biggest common factor number .

Step-1: Prime Factorization of 1985

Prime factors of 1985 are 5, 397. Prime factorization of 1985 in exponential form is:

1985 = 5¹ × 397¹

Step-2: Prime Factorization of 1995

Prime factors of 1995 are 3, 5, 7, 19. Prime factorization of 1995 in exponential form is:

1995 = 3¹ × 5¹ × 7¹ × 19¹

Step-3: Factors of 1985

List of positive integer factors of 1985 that divides 1985 without a remainder.

1, 5, 397

Step-4: Factors of 1995

List of positive integer factors of 1995 that divides 1985 without a remainder.

1, 3, 5, 7, 15, 19, 21, 35, 57, 95, 105, 133, 285, 399, 665

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1985 and 1995. The biggest common factor number is the GCF number.
So the greatest common factor 1985 and 1995 is 5.

Also check out the Least Common Multiple of 1985 and 1995