number between 80000 and 100000 divisible by 2, 3, 4, 5, 6, 9 and 10
Find a number inbetween 80000 and 100000 that is divisible by 2,3,4,5,6,9,10?
Multiply the factors of the divisors, without unnecessary duplicates.
2 * 3 * 2*2 * 5 * 2*3 * 3*3 * 2*5
We can eliminate one of the 2s in the 4 because we already have one
We can eliminate the 6: we already have 2 * 3
We can eliminate one of the 3s in the 9
We can eliminate the 10 because we already have a 2 and a 5
2 * 3 * 2 * 5 * 3
(You can see that we have 2 and 3; we also have 2*2, 4; we have 5;
we have 2*3, 6; we have 3*3, 9; and we have 2*5, 10.)
That gives us 180. Any multiple of 180 will be divisible by
all of the specified numbers.
Therefore, any of the multiples of 180 between 80000 and 100000 will
satisfy this problem statement.
The first one can be found by dividing 80000 by 180: 444.444444
We need the next whole number, 445, multiplied by 180: 80100
How many multiples of 180 are there between 80000 and 100000?
That's a span of 100000 - 80000 = 20000
How many times does 180 go into 20000? 20000/180 = 111.11111
There are 111 multiples of 180 in the given range. The first one
has already been calculated. Keep adding 180 to that and each
successive sum, and you will have as many answers to the
problem as you want.