The **divisors** of a number are the positive whole numbers that divide into it evenly. For example the divisors of 6 are: 1, 2, 3, and 6. Notice that 6 has **four** divisors. If you count how many divisors the number has your answer might be even (6 has **4** divisors) or it might be odd (1 has only **1** divisor, namely itself). How many of the numbers from 1 to 400 have an odd number of divisors?

Guest Jul 5, 2018

#2**0 **

The numbers with odd divisors under 400 are as follows:

1, 2^2, 2^4, 2^6, 2^8, 3^2, 3^4, 5^2, 6^2, 7^2, 10^2, 11^2, 12^2, 13^2, 14^2, 15^2, 17^2, 18^2, 19^2=19 numbers under 400.

The number of divisors of each of the above 19 numbers, with the exception of 1, is the exponent of that number + 1. Example: 2^8 has 8 + 1 = 9 divisors, because 2^8 = 256 which has:1 | 2 | 4 | 8 | 16 | 32 | 64 | 128 | 256 (9 divisors).....and so on. The ones with more than one factor, such as:18^2 =324 =2^2 x 3^4 =(2+1) x (4+1)=3 x 5 = 15 divisors.....and so on.

Guest Jul 6, 2018