Question 105741
Prime factorization is a mathematical process wherein you express a number a a product of prime factors.


Example:

What is the prime factorization of 200?

Since the smallest prime factor we know is 2, it is convenient to divide 200 continuously until the quotient obtained is not an integer.

200/2=100
100/2=50
50/2=25
25/2=not an integer(12.5)

So we proceed. The next prime no. is 3. However, 25 is not divisible by 3.So, the next prime is 5!

25/5=5
5/5=1

STOP!!! Since we have obtained 1, we will stop.

It the first part(dividing by 2) we divided 3 times (NOTE: 25/2 is not included)

So we write:

{{{2^3}}}

Last part (dividing by 5)---we divided 2 times.

So we annex this with the multiplication sign.thus,

{{{200=2^3*5^2}}}


For your problem!\

First, let's divide by 2!

330/2=165
We can not proceed because 165 is not divisible by 2.Next, let's divide by 3.

165/3=55

We can't proceed because 55 is not divisible by 3. Next, let's divide by 5!

55/5=11

We acn't proceed because 11 is not divisible by 5. 11, also, is not divisible by 7, the next prime number. So, let's divide by 11!

11/11=1

STOP!!!

dividing by 2---divided once. So immediately write

{{{2}}}

dividing by 3---divide once. Annex {{{3}}},
{{{2*3}}}

dividing by 5---divided once, too. Annex {{{5}}}

{{{2*3*5}}}

dividing by 11---divided once. Annexing {{{11}}}, Therefore,


{{{330=2*3*5*11}}}

This is the pime factorization of 330!


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