×

factoriaaaal!

33!=12^{x} * y

find maximum integral value of x

Note by G J
4 years, 3 months ago

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. list
1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in $$...$$ or $...$ to ensure proper formatting.
2 \times 3 $$2 \times 3$$
2^{34} $$2^{34}$$
a_{i-1} $$a_{i-1}$$
\frac{2}{3} $$\frac{2}{3}$$
\sqrt{2} $$\sqrt{2}$$
\sum_{i=1}^3 $$\sum_{i=1}^3$$
\sin \theta $$\sin \theta$$
\boxed{123} $$\boxed{123}$$

Sort by:

The maximum integral value of x is 15.

We consider the highest prime in order to make divisibility to the said number 33!.

Since 33! = 1. 2. 3. 4.... 31. 32. 33

The numbers divisible by 3 are 3, 6, 9, 12, 15,... 30, 33.

Taking the powers of 3 divisible by these numbers, the highest power of 3 that divides by 33! is 3^15.

Taking the powers of 2 from the even numbers, the highest power of 2 that divides 33! is 41.

Since 12^x = 2^(2x) . 3^x

The highest power of 12 that divides 33! is 15.

- 4 years, 3 months ago