# Maths Word Problem Homework

• Apr 27th 2009, 01:15 PM
bob
Maths Word Problem Homework

The first 100 positive whole numbers are multiplied together to form the number N.
(a) What is the very last right-hand (ie "units") digit of N? Explain your answer.
(b) What digit is in the 19th place from the right? Explain your answer.

Thank you.
• Apr 27th 2009, 01:37 PM
Unenlightened
Quote:

Originally Posted by bob

The first 100 positive whole numbers are multiplied together to form the number N.
(a) What is the very last right-hand (ie "units") digit of N? Explain your answer.
(b) What digit is in the 19th place from the right? Explain your answer.

Thank you.

The last digit has to be 0.
Since any whole number multiplied by, say, 10, equals zero.

And I think... the 19th may also be...
10,20,30,40,50,60,70,80,90,100 add in a zero, as do 5*2,12*15,22*25,32*35,42*45,52*55,62*65, 72*75, 82*85, & 92*95.

Aye, there's 20 of them. So the 19th place from the right is also a 0.
• Apr 27th 2009, 01:54 PM
bob
Hi Unenlightened, that was quick thank you very much you are a life saver.(Clapping)

Bob
• Apr 27th 2009, 01:59 PM
Plato
Notice that $N=100!$.
$100!$ has a factor of $5^{24}$.
So N has 24 'trailing' zeros. (Ends in 24 zeros.)
• Apr 28th 2009, 01:48 AM
bob
Hi Plato

Please would you explain how N=100. I was trying to multiply all the numbers together to get N.
• Apr 28th 2009, 02:46 AM
Air
Quote:

Originally Posted by bob

The first 100 positive whole numbers are multiplied together to form the number N.
(a) What is the very last right-hand (ie "units") digit of N? Explain your answer.
(b) What digit is in the 19th place from the right? Explain your answer.

Thank you.

Multiplying the first $100$ numbers means that you are doing the factorial of $100$. $100! = 100 \times 99 \time 98 \times ... \times 1$.

(a) Lets say you did $99 \time 98 \times ... \times 1$ and last step was to multiply be $100$ to get $100!$. If you multiply any number by $100$, what is the last digit?

(b) Try to understand how many zeros that $100!$ has then you many be able to work out what the 19th value is.

Spoiler:
This website talks about $100!$, giving it's value and explaining how many zero's it has.

• Apr 28th 2009, 02:48 AM
Plato
Quote:

Originally Posted by bob
Please would you explain how N=100. I was trying to multiply all the numbers together to get N.

You don't understand. That is 100!, one hundred factorial.
Like $5!=(5)(4)(3)(2)(1)=120$.
• Apr 28th 2009, 03:39 AM
bob
Hi Air and Plato

Thanks for explaining.

I've just started factors at school, it is taking me a little while to understand the topic properly.