How many composite numbers are between 1 and 100?
2 Answers
Explanation:
Note that the following answer assumes that "between 1 and 100" is intended to include
Start with the numbers

#1# is not composite, because it's a unit, so that leaves#99# other numbers. 
The numbers
#4=2^2, 6, 8, ... , 100# are all divisible by#2# , so composite. There are#(1004)/2+1 = 49# of these, leaving#9949 = 50# other numbers. 
The numbers
#9=3^2, 15, 21,..., 99# are all divisible by#3# and not by#2# . There are#(999)/6+1 = 16# of these, leaving#5016 = 34# other numbers. 
The numbers
#25=5^2, 35, 55, 65, 85, 95# are all divisible by#5# and not by#2# or#3# . There are#6# of these, leaving#346 = 28# other numbers. 
The numbers
#49=7^2, 77, 91# are divisible by#7# and not by#2# ,#3# or#5# . There are#3# of these, leaving#283 = 25# other numbers.
These
So the total number of composite numbers is:
#49+16+6+3 = 74#
There are
Explanation:
There are
However, the question specifies numbers BETWEEN
So we are left with
All the numbers between
(The only number that is neither is
There are
This is pretty easy to check by just counting them, but it is a small fact that is worth knowing.
Therefore, if