Math Help - Need Urgent Help i'm unsure

1. Need Urgent Help i'm unsure

hey guys I need help with a problem concerning factors and a 3 digit number. I had the answer to this question as 891 using some algebra but my friend got a higher 3 digit number than me. Any help for the below question will be welcomed with open arms.

Find the largest 3 digit number which has exactly 10 factors including 1 and itself.

Yeah I have 891...is there a higher 3 digit number with 10 factors?

***

i think i have the number i just need 2 know how to work it out so i can check

2. Originally Posted by math_spartan
hey guys I need help with a problem concerning factors and a 3 digit number. I had the answer to this question as 891 using some algebra but my friend got a higher 3 digit number than me. Any help for the below question will be welcomed with open arms.

Find the largest 3 digit number which has exactly 10 factors including 1 and itself.

Yeah I have 891...is there a higher 3 digit number with 10 factors?

***

i think i have the number i just need 2 know how to work it out so i can check
I think the number is 976

3. me 2

Originally Posted by malaygoel
I think the number is 976
so do I...THe factors for 976 are 1 2 4 8 16 61 122 244 488 976. Hey malaygoel how did you work it out? I'm interested in different methods of working.

4. Originally Posted by mathemagician
so do I...THe factors for 976 are 1 2 4 8 16 61 122 244 488 976. Hey malaygoel how did you work it out? I'm interested in different methods of working.
Do you know how to find the no. of factors of a given number?

5. no not really

no not really...i used a factor calculator thing on the internet...can u tell me how to find the no. of factors for a given number...please?

6. Originally Posted by math_spartan
hey guys I need help with a problem concerning factors and a 3 digit number. I had the answer to this question as 891 using some algebra but my friend got a higher 3 digit number than me. Any help for the below question will be welcomed with open arms.

Find the largest 3 digit number which has exactly 10 factors including 1 and itself.

Yeah I have 891...is there a higher 3 digit number with 10 factors?

***

i think i have the number i just need 2 know how to work it out so i can check
Consider a number $N$ with prime factorisation

$N=p_1^{n_1}p_2^{n_2}\dots p_m^{n_m}$,

then the number of divisors of $N$ is:

$d(N)=\prod_1^{m}(1+n_m)$.

If $d(N)=10$, then either $N$ is a ninth power of a single prime,
or it a product of a prime and a fourth power of another prime (as 10 only
has factorisations 1x10 and 2x5).

If $N<1000$, in the first of these cases the only possible candidate for the
prime is $2$, and so then $N=2^9=512$.

If $N<1000$, in the second of these cases the only possible candidates for the
prime raised to the fourth power are $2,\ 3,\ 4$. Then trial and
error shows that the largest $N<1000$ that is a prime times the
fourth power of one of these primes is:

$
N=61\times 2^4=976
$

RonL

7. Originally Posted by CaptainBlack
...
$
N=91\times 2^4=976
$

RonL
Hello,

you calculated $N=61\times 2^4=976$, which fits better to your explanations.

Greetings

EB

8. Originally Posted by earboth
Hello,

you calculated $N=61\times 2^4=976$, which fits better to your explanations.

Greetings

EB

Opps..

Must remember not to use that Escher note paper for scribbling down results
in future

RonL

9. Originally Posted by CaptainBlack
Opps..
Must remember not to use that Escher note paper for scribbling down results
in future
RonL
Hello,

if you are still using this kind of note paper you should better change your scribbling practice (see attachment).

(By the way where did you know it from that Mijnheer M. C. Escher is one of my favourite artists? Or has the stealth group of this forum already scanned and cataloguized my personality, so there won't be any personality left?).

Greetings

EB

10. Originally Posted by earboth
Hello,

if you are still using this kind of note paper you should better change your scribbling practice (see attachment).

(By the way where did you know it from that Mijnheer M. C. Escher is one of my favourite artists? Or has the stealth group of this forum already scanned and cataloguized my personality, so there won't be any personality left?).

Greetings

EB
I didn't know he was one of you favourite artist, it just so happens that