Question

It is desired to extract the maximum power of 3 from 24!, where n! = n.(n 1) . (n 2) 3.2.1. What will be the exponent of 3?

Answer 1

Answer:

10 factors

Step-by-step explanation:

an logarithm that always works is to repeatedly divide 24 by 3, to count the number of 3's in the factorization. for example,

24/3 = 8

8/3 = 2 (excluding remainders)

2/3 = 0

there are 8+2+0 = 10 factors of 3.

Answer 2

Given:

24!

To find:

Exponent of 3

Solution:

24!=$24\cdot 23\cdot 22\cdot 21...3\cdot 2\cdot 1$

$24!=(3\times 8)\times 23\times 22\times (3\times 7)\times 20\times 19\times (3^2\times 2)\times 17\times 16\times (3\times 5)\times 14\times 13\times (3\times 4)\times 11\times 10\times 3^2\times 8\times 7\times (3\times 2)\times 5\times 4\times 3\times 2\times 1$

24!=$3^{10}\times 8\times 23\times 22\times 7\times 20\times 19\times 2\times 17\times 16\times 5\times 14\times 13\times 4\times 11\times 10\times 8\times 7\times 2\times 5\times 4\times 2\times 1$

Therefore, the exponent of 3=10