Question

How many numbers less than1000 which have more than 24 factors?

Answer 1

prime factors?

Answer 2

24 factors?
are we talking about positive factors or both neg and pos?

Answer 3

All positive factors including prime or nonprime

Answer 4

are you sure you didn't make this question up yourself

Answer 5

24 factors?
are we talking about positive factors or both neg and pos?

Answer 6

i will think on it but i have to leave for now

Answer 7

This question ask me in test

Answer 8

Any one try it

Answer 9

i think its answer is zero.

Answer 10

Actually 0 is right. 2^24>1000

Answer 11

the least prime factors is 2 & 3
so when we taken 2^7 x 3^2 which is greater than 1000
so we take 2^7 x 3^1 which is 384 less than 1000
than calculate all factors i.e. 8x2=16 which is not greater than 24
and there is no any combination is to be formed with any prime factors by which there we get more than 24 factors.
but i want direct trick for getting this.

Answer 12

2^24 is also greater than 2000, 5000, 10000, 100000 so how can u say that
while 1080 has 32 factors

Answer 13

2^24 has 24 factors and is greater than 1000
so you have the empty set is answer

Answer 14

2^24 has 25 factors

Answer 15

actually it has 26

Answer 16

actually is has more lol

Answer 17

1
2,2,2,2,....
4
8
16
...
2^24

Answer 18

i dont know the answer to this question anymore

Answer 19

my dear friend 2^24 has 25 factors only

Answer 20

yes you are right but 2^23>1000 and has 24 factors

Answer 21

Yeah that was my problem with it myin. If it was just to count the multiplicity of the prime factors there aren't any, if we take all the possible combinations of all the possible factors it seemed like a very complex problem.

Answer 22

right lol

Answer 23

hello friends i have found 3 numbers of which there is more than 24 factors

Answer 24

and these numbers are less than 1000

Answer 25

first number is: 2^3x3^1x5^1x7^1=840 & it has 4x2x2x2=32 total factors
second number is: 2^6x3^1x5^1=480 & it has 7x2x2=28 total factors
third number is: 2^4x3^2x5^1=720 & it has 5x3x2=30 total factors

and i am sure that there is no any more no accept these three i.e. 480, 720, & 840 less than 1000 which have more than 24 factors.

if anybody can find any more then tell to me

Answer 26

i found 2 more numbers
so there has total 5 numbers less than 1000 which has more than 24 factors

720-> 2^4*3^2*5^1
810-> 2^1*3^4*5^1
840-> 2^3*3^1*5^1*7^1
900-> 2^2*3^2*5^2
960-> 2^6*3^1*5*1