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How many integers are between 1000 and 10000?
9000 integers.
How many positive integers less than 100 have an odd number of positive divisors?
The squares -- nine of them.
How many positive integers less than or equal to 100 have a prime factor that is greater than 4?
There are 80 such integers.
How many positive integers less then 50 are multiples of 4 but not multiples of 6?
10
How many pairs of consecutive integers have a product less than 10000?
n(n+1) <10000 so n is close to square-root of 10000 which is 100. Obviously 100x101 is too much, but 99x100 is OK
How many positive integers less than or equal to 10000 are divisible by 2 5 or 10?
To find how many positive integers less than or equal to 10,000 are divisible by 2, 5, or 10, we can use the principle of inclusion-exclusion. The count of integers divisible by each is: Divisible by 2: ( \frac{10000}{2} = 5000 ) Divisible by 5: ( \frac{10000}{5} = 2000 ) Divisible by 10: ( \frac{10000}{10} = 1000 ) Applying inclusion-exclusion, we have: [ 5000 + 2000 - 1000 = 6000 ] Thus, there are 6000 positive integers less than or equal to 10,000 that are divisible by 2, 5, or 10.
How many positive odd integers less than 10000 can be written using the digits 3 4 6 8 and 0?
125
How many positive integers are less then 50?
49
How many positive integers less than 1000 are not divisible by 3?
666 integers.
How many positive integers less than 2010 have an odd number of factors?
There are 44 positive integers less than 2,010 that have an odd number of factors.
How many positive integers less than 1000 are divisible by 7 and are not divisible by 11?
There are 130 positive integers less than 1,000 that are divisible by seven but not divisible by 11
How many positive integers less than 1000 are either divisible by 2 or by 11?
There are 544 positive integers less than 1,000 that are either divisible by two or by 11.
How many positive integers less than 20 are prime?
Eight.
How many positive integers less than 200 are divisible by 2 3 5?
6
How many integers are between 1000 and 10000?
9000 integers.
How many positive integers less than 100 have an odd number of positive divisors?
The squares -- nine of them.
How many elements are there in the set of positive integers less than 8?
7 of them.
