SBP-Program

19992 prime factorization

What is the prime factorization of 19992?

Find the prime factorization of 19992

We draw a vertical line and write 19992 to the left of the line:

 19992

19992 is divisible by 7

19992 : 7 = 2856

We write 7 (the divisor) to the right of the line and 2856 to the left of the line:

 19992 7 2856

7 is a prime number.

2856 is not a prime number.

2856 is divisible by 7:

2856 : 7 = 408

We write 7 (the divisor) to the right of the line and 408 to the left of the line:

 19992 7 2856 7 408

408 is divisible by 6:

408 : 6 =
408 : (2 * 3) = 68

We write (2 * 3) (the divisor) to the right of the line and 68 to the left of the line:

 19992 7 2856 7 408 2 * 3 68

68 is divisible by 4:

68 : 4 = 68 : (2 * 2) = 17

We write (2 * 2) (the divisor) to the right of the line and 17 to the left of the line:

 19992 7 2856 7 408 2 * 3 68 2 * 2 17

17 is a prime number. 17 is divisible by itself and by 1. We divide 17 by 17:

17 : 17 = 1

and write 17 (the divisor) to the right of the line and 1 to the left of the line:

 19992 7 2856 7 408 2 * 3 68 2 * 2 17 17 1

The numbers to the right of the line are prime factors of the number 19992.

Therefore, the prime factorization of 19992 is

19992 =
2 * 2 * 2 * 3 * 7 * 7 * 17

The prime factorization of 19992 using exponents

19992 =
23 * 3 * 72 * 17

So, the prime factors of 19992 are

2, 2, 2, 3, 7, 7, 17