Raymond B. answered • 01/31/24
Math, microeconomics or criminal justice
from 1 to 1,000 half are divisible by 2, all the even numbers, that's 500 numbers
from 1 to 1,000 1/3 are divisible by 3. 3,6,9,12,15,18, 21, 24,27, 30,33,336,339, 342,345,348 ... 990,993, 996, 999, that's 333 numbers
to be divisible by 6 means to be divisible by both 2 and 3: 6, 12, 18, 24, 30, ... that's 1/3 x 1/2 = 1/6 of the numbers or about 1000/6 = 167 numbers
to be divisible by 9 means 1 out of 9 or 1/9 of the numbers = about 1000/9 = 111 numbers
9,18,27,36,45, ... 999
divisible by 6 or 9 means 167 + 111 - overlap = 278 - overlap
the overlap are those numbers divisible by 6 and 9. 18, 36, 54... those numbers divisible by 18: that's 1/18 or about 1000/18 = about 55
278-55 = 223 numbers
divisible by neither 6 nor 9 means
1000-223 = 777 numbers
1,2,3,4,5,7,8,
10,11, 13,14,15,16,17, 19
20,21,22,23,25,26,28,29
...
