what is the number?

Question

what is the number that its half and its quarter and its 1/3 ,and its 1/5 ,and its 1/6 , and its 1/8 and 1/9 is an integer ......

Answer 1

360 and its multiples (including 0 :P)

Answer 2

If its 1/8 is an integer, its 1/4 and 1/2 are automatically integers since they are multiples of each other (anything divisible by 8 is also divisible by 4 and 2)

If its 1/9 is an integer, its 1/3 is automatically an integer since they are multiples of each other. (anything divisible by 9 is also divisible by 3)

Start with 9 x 8 x 5 = 72 x 5 = 360.
360/9 = 40
360/8 = 45
360/6 = 60
360/5 = 72
360/4 = 90
360/3 = 120
360/2 = 180

Answer 3

Another way to ask this question is:

What number is evenly divisible (without remainder) by 2,3,4,5,6,8 and 9?

A couple of simplifications to this:
- Any number that is evenly divisible by 9 is also evenly divisible by 3.
- Any number that is evenly divisible by 8 is also evenly divisible by 4 and 2.
- Any number that is evenly divisible by both 8 and 9 is also evenly divisible by 6 (since it is divisible by 2 and 3).

So, we are looking for an integer evenly divisible by 5,8 and 9.

One quick way to create such an integer is to multiply those numbers together.

Therefore:
5*8*9 = 360

1/2 of 360 = 180
1/3 of 360 = 120
1/4 of 360 = 90
1/5 of 360 = 72
1/6 of 360 = 60
1/8 of 360 = 45
1/9 of 360 = 40

Any multiple of 360 (i.e., 720, 1080, etc) would also have the same property.

Answer 4

2 * 3 * 4 * 5 * 6 * 7 * 8 * 9 = 362 880

Is there are smaller number that does this as well?

3*5*7*8*9 = 7 560 (the eight and nine represent 2 & 3 multiples as well).

Answer 5

it is= 2 * 2 * 2 * 3 * 3 * 5

So the integer is=360

Answer 6

360

Answer 7

1 = 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64...

Answer 8

waaaaaaaaaaaaaat?