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There are 9 integers less than 100 that have an odd number of factors.
Every factor of a number has a pair, eg 2 & 3 are a factor pair of 6; and so it would be expected that every number has an even number of factors.
However, if the factor pair of a number are the same number (eg 6 & 6 are a factor pair of 36), then there will be an odd number of factors.
When there is a repeated factor like this, the number is a perfect square.
Thus only perfect squares have an odd number of factors.
Less than 100 there are 9 perfect squares (1, 4, 9, 16, 25, 36, 49, 64 & 81) which have an odd number of factors.
100 itself is a perfect square and also has an odd number of factors, but the question asked for those numbers less than 100 with an odd number of factors.
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How many positive integers less than 100 have an odd number of positive divisors?
The squares -- nine of them.
How many numbers which are less than 1000 have an odd number of factors?
Perfect squares have an odd number of factors. There are 31 perfect squares less than 1000.
How many positive integers are there less than 10000?
One less than 10000.
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 integers are there?
an infinite number. integers are all whole numbers, negative numbers and positive numbers.
