How many three-digit numbers have an odd number of factors?
Answers
Given : three-digit numbers
To Find : How many three-digit numbers have an odd number of factors
Solution:
In general factor are in pairs
Like for a number n
n = a * b = c * d = _____
Hence factors are in even numbers
but if there is one factor
n = k * k also with other factor
Then this will be 1 factor ( odd number )
even + odd = odd
Hence total number of factors will be odd
n = k ²
Hence number must be a perfect square
Properties of number that the number of factors come as an odd number is that Number must be a perfect square
100 to 999 are 3 digit numbers
100 is perfect square of 10
961 is perfect square of 31
Then 32² = 1024 > 999
Hence Square of numbers from 10 to 31 are three-digit numbers , which have odd number of factors
Hence there are 22 Such numbers
22 Three-digit numbers have an odd number of factors
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Answer:
In general factor are in pairs
Like for a number n
n = a*b =c*d =
Hence factors are in even numbers
but if there is one factor
n = k* k also with other factor Then this will be 1 factor (odd number)
even + odd = odd
Hence total number of factors will be odd
n = k ^ 2
Hence number must be a perfect square.
Properties of number that the number of factors come as an odd number is that Number must be a perfect square.
100 to 999 are 3 digit numbers.
100 is perfect square of 10 961 is perfect square of 31
Then 32² = 1024 > 999.
Hence Square of numbers from 10 to 31 are three-digit numbers, which have odd number of factors.
Hence there are 22 Such numbers.
22 Three-digit numbers have an odd number of factors.