What is the Greatest Common Factor of 19965 and 19984?

Greatest common factor (GCF) of 19965 and 19984 is 1.

GCF(19965,19984) = 1

We will now calculate the prime factors of 19965 and 19984, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19965 and 19984.

How to find the GCF of 19965 and 19984?

We will first find the prime factorization of 19965 and 19984. After we will calculate the factors of 19965 and 19984 and find the biggest common factor number .

Step-1: Prime Factorization of 19965

Prime factors of 19965 are 3, 5, 11. Prime factorization of 19965 in exponential form is:

19965 = 3¹ × 5¹ × 11³

Step-2: Prime Factorization of 19984

Prime factors of 19984 are 2, 1249. Prime factorization of 19984 in exponential form is:

19984 = 2⁴ × 1249¹

Step-3: Factors of 19965

List of positive integer factors of 19965 that divides 19965 without a remainder.

1, 3, 5, 11, 15, 33, 55, 121, 165, 363, 605, 1331, 1815, 3993, 6655

Step-4: Factors of 19984

List of positive integer factors of 19984 that divides 19965 without a remainder.

1, 2, 4, 8, 16, 1249, 2498, 4996, 9992

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19965 and 19984. The biggest common factor number is the GCF number.
So the greatest common factor 19965 and 19984 is 1.

Also check out the Least Common Multiple of 19965 and 19984