# Thread: Maths Word Problem Homework

1. ## 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.

2. 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.

3. Hi Unenlightened, that was quick thank you very much you are a life saver.

Bob

4. Notice that $\displaystyle N=100!$.
$\displaystyle 100!$ has a factor of $\displaystyle 5^{24}$.
So N has 24 'trailing' zeros. (Ends in 24 zeros.)

5. Hi Plato

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

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

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

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

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

7. 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 $\displaystyle 5!=(5)(4)(3)(2)(1)=120$.

8. 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.