What is the Greatest Common Factor of 17965 and 17970?

Greatest common factor (GCF) of 17965 and 17970 is 5.

GCF(17965,17970) = 5

We will now calculate the prime factors of 17965 and 17970, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17965 and 17970.

How to find the GCF of 17965 and 17970?

We will first find the prime factorization of 17965 and 17970. After we will calculate the factors of 17965 and 17970 and find the biggest common factor number .

Step-1: Prime Factorization of 17965

Prime factors of 17965 are 5, 3593. Prime factorization of 17965 in exponential form is:

17965 = 5¹ × 3593¹

Step-2: Prime Factorization of 17970

Prime factors of 17970 are 2, 3, 5, 599. Prime factorization of 17970 in exponential form is:

17970 = 2¹ × 3¹ × 5¹ × 599¹

Step-3: Factors of 17965

List of positive integer factors of 17965 that divides 17965 without a remainder.

1, 5, 3593

Step-4: Factors of 17970

List of positive integer factors of 17970 that divides 17965 without a remainder.

1, 2, 3, 5, 6, 10, 15, 30, 599, 1198, 1797, 2995, 3594, 5990, 8985

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17965 and 17970. The biggest common factor number is the GCF number.
So the greatest common factor 17965 and 17970 is 5.

Also check out the Least Common Multiple of 17965 and 17970