What is the Greatest Common Factor of 61965 and 61982?

Greatest common factor (GCF) of 61965 and 61982 is 17.

GCF(61965,61982) = 17

We will now calculate the prime factors of 61965 and 61982, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 61965 and 61982.

How to find the GCF of 61965 and 61982?

We will first find the prime factorization of 61965 and 61982. After we will calculate the factors of 61965 and 61982 and find the biggest common factor number .

Step-1: Prime Factorization of 61965

Prime factors of 61965 are 3, 5, 17. Prime factorization of 61965 in exponential form is:

61965 = 3⁶ × 5¹ × 17¹

Step-2: Prime Factorization of 61982

Prime factors of 61982 are 2, 17, 1823. Prime factorization of 61982 in exponential form is:

61982 = 2¹ × 17¹ × 1823¹

Step-3: Factors of 61965

List of positive integer factors of 61965 that divides 61965 without a remainder.

1, 3, 5, 9, 15, 17, 27, 45, 51, 81, 85, 135, 153, 243, 255, 405, 459, 729, 765, 1215, 1377, 2295, 3645, 4131, 6885, 12393, 20655

Step-4: Factors of 61982

List of positive integer factors of 61982 that divides 61965 without a remainder.

1, 2, 17, 34, 1823, 3646, 30991

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 61965 and 61982. The biggest common factor number is the GCF number.
So the greatest common factor 61965 and 61982 is 17.

Also check out the Least Common Multiple of 61965 and 61982