fenders -- srsli difficult

• Jun 2nd 2006, 08:45 PM
phatjigga
fenders -- srsli difficult
hey guys

could u guys hav a read of this q? coz its a monster one!!! so hard... siigh
neway dis is da q..

an eg:
choose a number:156
its factors are: 1,2,3,4,6,12,13,26,39,52,78,156
grouped by last digit:{1}, {2,12,52}, {3,13}, {4}, {6,26,156}, {78}, {39}

We say the fenders (factor enders) of 156 are 1,2,3,4,6,8,9 and that 156 is a 7-fender (meaning dat it had seven fenders)

a) find a 1-fender which is composite
b) Show that a number which has a 0 and a 9 as fenders has at least four more fenders
c) the smallest 10 fender is less thaan 700. Find it and explain why is is the smallest

Another 7-fender is 460--its set of fenders is (0,1,2,3,4,5,6,); which is different from the set of fenders of 156
d) find three 9-fenders less than 1000 with different sets of fenders

yea...its reeli hard... i hardly evn understand the q....
plz try dis q!!
any help would be like a call from heaven!!! lol :P
thanx soooo much guys
• Jun 2nd 2006, 09:28 PM
CaptainBlack
Quote:

Originally Posted by phatjigga
hey guys

could u guys hav a read of this q? coz its a monster one!!! so hard... siigh
neway dis is da q..

an eg:
choose a number:156
its factors are: 1,2,3,4,6,12,13,26,39,52,78,156
grouped by last digit:{1}, {2,12,52}, {3,13}, {4}, {6,26,156}, {78}, {39}

We say the fenders (factor enders) of 156 are 1,2,3,4,6,8,9 and that 156 is a 7-fender (meaning dat it had seven fenders)

a) find a 1-fender which is composite

As 1 is a factor of every number, every factor of of a 1-fender must end in a
1. Now if \$\displaystyle p\$ is a prime ending in a 1, then p is a 1-fender, but not composite
(composite means it has more factors that 1 and itself).

Let \$\displaystyle p\$ be a prime ending in a 1, what is the last digit of \$\displaystyle p^2\$? What are the
factors of \$\displaystyle p^2\$ (which is composite)?

RonL

RonL
• Jun 2nd 2006, 09:59 PM
phatjigga
thanx now i understand (a) but can anyone help me with the other ones?
hey could neone be able to help me with b,c or d??
thanx captain black 4 helping me with a.
i stilll dont understand the other qs
any help would be wonderful
thanks guys
• Jun 2nd 2006, 10:06 PM
CaptainBlack
Quote:

Originally Posted by phatjigga
hey guys

could u guys hav a read of this q? coz its a monster one!!! so hard... siigh
neway dis is da q..

an eg:
choose a number:156
its factors are: 1,2,3,4,6,12,13,26,39,52,78,156
grouped by last digit:{1}, {2,12,52}, {3,13}, {4}, {6,26,156}, {78}, {39}

We say the fenders (factor enders) of 156 are 1,2,3,4,6,8,9 and that 156 is a 7-fender (meaning dat it had seven fenders)

b) Show that a number which has a 0 and a 9 as fenders has at least four more fenders

A number with 0 as a fender is divisible by 10, and so is divisible by all of
the factors of 10, and hence has as fenders the last digits of all of the
factors of 10 (2 is a factor of 10 and hence one of the fenders of any
number with 0 as a fender). (since all the factors of 10 have a single digit
they are in fact fenders)

A number with a fender of 9 has a factor \$\displaystyle x\$with last digit 9, and as 2 is a
factor of our number with fenders 0 and 9, so is \$\displaystyle 2x\$. What is the fender of \$\displaystyle 2x\$?

RonL

Having got this far how many new fenders have you found?
• Jun 2nd 2006, 10:17 PM
phatjigga
umm..
Quote:

Originally Posted by CaptainBlack
A number with 0 as a fender is divisible by 10, and so is divisible by all of
the factors of 10, and hence has as fenders the last digits of all of the
factors of 10 (2 is a factor of 10 and hence one of the fenders of any
number with 0 as a fender). (since all the factors of 10 have a single digit
they are in fact fenders)

A number with a fender of 9 has a factor \$\displaystyle x\$with last digit 9, and as 2 is a
factor of our number with fenders 0 and 9, so is \$\displaystyle 2x\$. What is the fender of \$\displaystyle 2x\$?

RonL

Having got this far how many new fenders have you found?

to be truly honest, i hav absolutely no idea captain black :o :confused:
i understand (a) quite well but then (b) .... im totally confused
sorry....
if it wouldnt be too much of a bother, could you please explain it to me again??
thank you sooo much :)
• Jun 2nd 2006, 10:39 PM
CaptainBlack
Quote:

Originally Posted by phatjigga
to be truly honest, i hav absolutely no idea captain black :o :confused:
i understand (a) quite well but then (b) .... im totally confused
sorry....
if it wouldnt be too much of a bother, could you please explain it to me again??
thank you sooo much :)

The only way a number can have 0 as a fender is if it has a factor ending
in a 0. A number ending in a 0 is divisible by 10, like 10, 20 ,30, ..

But if a number is divisible by 10, it is divisible by all the proper divisors of 10
which are 1, 2 and 5

These divisors all have 1-digit, and so are fenders of the original number.

Thus we already have three new fenders of our original number.

If the original number has 9 as a fender it has a factor with last
digit 9, call this \$\displaystyle x\$, now as 2 is also a factor of our original
number so is \$\displaystyle 2x\$.

What is the last digit of \$\displaystyle 2x\$? It is a fender of the original number,
but is it different from the fenders we already have found?

RonL
• Jun 3rd 2006, 08:01 AM
Joyce
where is my question????
:confused: :confused: :confused:
• Jun 3rd 2006, 08:22 AM
CaptainBlack
Quote:

Originally Posted by Joyce
where is my question????
:confused: :confused: :confused:

It is deleted. I have told you already not to tag questions onto the
end of existing threads, but to create new threads (in an appropriate
forum -urgent homework, or trigonometry would seem to be appropriate) for
new questions.

To create a new thread open a forum. There will be a button near the
top on the left labelled "new thread", hit that and you will be able to