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What is a number that you odd less than 20 but is a multiple of 5?
'5' & '15' are odd numbers less than 20 , and are also multiples of '5'.
What is a multiple of 10 includes an even and odd number and is more than 3x5 and is less than 4x7?
4 x 5
How many positive integers less than 100 have an odd number of positive divisors?
The squares -- nine of them.
How many integers less than 100 have an odd number of factors?
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.
How do you calculate the 100th odd number?
1st odd number . . . 1 (1 less than double 1)2nd odd number . . . 3 (1 less than double 2)3rd odd number . . . 5 (1 less than double 3)4th odd number . . . 7 (1 less than double 4)5th odd number . . . 9 (1 less than double 5)Are you seeing a pattern yet ?6th odd number . . . 11 (1 less than double 6)7th odd number . . . 13 (1 less than double 7)...Qth odd number . . . . (1 less than double Q)
