Question

Find the number of positive integers factors (excluding 1 and the number itself) of each of the following numbers:
a)3960
b)98010

Answer 1

For a) I got 6 and for b) i got 8. Can someone check if those are right?

Answer 2

for a) 2*2*2*3*3*5*11=3960
b) 2*3*3*3*3*5*11*11=98010

Answer 3

how did you get 6 for a ?

Answer 4

well there are three 2's, two 3's, one 5, and one 11, total of 6 factors
for b) there is one 2, four 3's, one 5, and two 11's, total of 8 factors?

Answer 5

a factor is a number that divides the number evenly

Answer 6

oh my bad 7 factrs

Answer 7

`n = a*b`

`a` and `b` are factors of `n`

Answer 8

2*2*2*3*3*5*11=3960

Notice that 2 is a factor of 3960
and so is 2*2

Answer 9

2*2*2*3 is also a factor

Answer 10

you need to consider all the combinations

Answer 11

so yea, for a) there are 7 factors and for b) there are 8

Answer 12

can you list all the 7 factors for a ?

Answer 13

you should get more than 7 for a

Answer 14

2x1980
2x2x990
2x2x2x495
2x2x2x3x165
2x2x2x3x3x55
2x2x2x3x3x5x11 <--7 factors

Answer 15

u just need to know number of factors theorem -.-

Answer 16

i dont see any factors in your list however all those are same as 3960

Answer 17

is it in ur txt book ?

Answer 18

This is handout for my teacher, not in the textbook

Answer 19

here is a list of all factors including 1 and the number itself

http://www.wolframalpha.com/input/?i=divisors+3960

Answer 20

so wait would these be the factors 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 15, 18, 20, 22, 24, 30, 33, 36, 40, 44, 45, 55, 60, 66, 72, 88, 90, 99, 110, 120, 132, 165, 180, 198, 220, 264, 330, 360, 396, 440, 495, 660, 792, 990, 1320, 1980, ooooh okay, i get it, i have to list all the multiples

Answer 21

-.-

Answer 22

you don't need to list all the factors,
you just need to give them the total number of factors

Answer 23

oh okay, i get it, thanks guys

Answer 24

So for the first there are 11 factors right?

Answer 25

how 11 ?

Answer 26

oh my bad 48 factors

Answer 27

that includes 1 and 3960

Answer 28

so 46 then

Answer 29

but they don't want them in the list so subtract 2

Answer 30

yes!

Answer 31

but how can you find the count without using wolfram ?

Answer 32

that i don't know

Answer 33

can you teach me?

Answer 34

its easy

Answer 35

whats the prime factorization of 3960 ?

Answer 36

2*2*2*3*3*5*11

Answer 37

write it in exponent form

Answer 38

(2^3)(3^2)(5^1)(11^1)

Answer 39

\[\large 3960 = 2^{\color{Red}{3}}3^{\color{Red}{2}}5^{\color{Red}{1}}11^{\color{red}{1}}\]

Answer 40

right

Answer 41

now consider a factor, it can have an exponent of 2 in 0,1,2,3 ways right ?

Answer 42

yes

Answer 43

it can have an exponent of 3 in 0,1,2 ways

Answer 44

it can have an exponent of 5 in 0,1 ways

Answer 45

it can have an exponent of 11 in 0,1 ways

Answer 46

oh okay, so when you multiply the choices you get 48

Answer 47

so the number of ways of choosing the exponents of prime numbers in a divisor is :
\[\large \color{Red}{(3+1)(2+1)(1+1)(1+1)}\]

Answer 48

exactly!

Answer 49

okay i get it, thats what i was missing

Answer 50

try to find the number of factors of number in part b using combinations

Answer 51

98010=(2^1)(3^4)(5^1)(11^2)
there are 60 factors of 98010 right?

Answer 52

Looks perfect!
not that you need to subtract 2 factors since the questions asks you to exclude 1 and the number itself

Answer 53

the count 60 includes both 1 and 98010 :

\(\large 1 = 2^03^05^011^0\)

\(\large 98010 = 2^13^45^111^3\)

Answer 54

oh okay so you subtract 2

Answer 55

yes

Answer 56

Thanks for the help everyone :D