<PRE><B>Question 1106561</B>

24 = {{{ 2^3*3 }}}

So any number without a factor of 2 or 3 will be relatively prime with 24.

The two digit numbers that meet this requirement are (more easily) found by eliminating those with 2 and 3 as factors: 

   2:  All even numbers
   3 (odd numbers shown):  15, 21, 27, 33, 39, 45, 51, 57, 63, 69, 75, 81, 87, 93, 99


Number of two-digit numbers =  99 - 10  + 1 = 90
Take away the even numbers leaves 45 numbers
Take away the 15 odd multiples of 3 leaves 30 numbers

—
Answer:  30 two digit numbers are relatively prime to 24
—
Check:   11,13,17,19,23,25,29,31,35,37,
              41,43,47,49,53,55,59,61,65,67,
              71,73,77,79,83,85,89,91,95,97

are all relatively prime to 24, and are all the two digit numbers not divisible by 2 or 3.   

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