What is the Greatest Common Factor of 19992 and 20009?

Greatest common factor (GCF) of 19992 and 20009 is 17.

GCF(19992,20009) = 17

We will now calculate the prime factors of 19992 and 20009, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19992 and 20009.

How to find the GCF of 19992 and 20009?

We will first find the prime factorization of 19992 and 20009. After we will calculate the factors of 19992 and 20009 and find the biggest common factor number .

Step-1: Prime Factorization of 19992

Prime factors of 19992 are 2, 3, 7, 17. Prime factorization of 19992 in exponential form is:

19992 = 2³ × 3¹ × 7² × 17¹

Step-2: Prime Factorization of 20009

Prime factors of 20009 are 11, 17, 107. Prime factorization of 20009 in exponential form is:

20009 = 11¹ × 17¹ × 107¹

Step-3: Factors of 19992

List of positive integer factors of 19992 that divides 19992 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 17, 21, 24, 28, 34, 42, 49, 51, 56, 68, 84, 98, 102, 119, 136, 147, 168, 196, 204, 238, 294, 357, 392, 408, 476, 588, 714, 833, 952, 1176, 1428, 1666, 2499, 2856, 3332, 4998, 6664, 9996

Step-4: Factors of 20009

List of positive integer factors of 20009 that divides 19992 without a remainder.

1, 11, 17, 107, 187, 1177, 1819

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19992 and 20009. The biggest common factor number is the GCF number.
So the greatest common factor 19992 and 20009 is 17.

Also check out the Least Common Multiple of 19992 and 20009