Not A Lot
Number Theory
Level
4
How many integers from 1 to 100 inclusive are not a
- prime nor
- multiple of 2 nor
- multiple of 3 nor
- multiple of 5?
1
4
2
3
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1 solution
The first is number 1, which is not considered to be a prime number. The rest must be multiples of at least two prime numbers. With 2, 3, and 5 excluded, they need to be multiples of 7. (Since 1 1 × 1 1 = 1 2 1 .) Only 7 × 7 , 7 × 1 1 , and 7 × 1 3 fall into the given size range.