SOLUTION: Two positive integers are relatively prime if they have no common factor other than 1. How many two-digit numbers are relatively prime with 24?

Question 1106561: Two positive integers are relatively prime if they have no common factor other than 1. How many two-digit numbers are relatively prime with 24?
Answer by math_helper(2461) (Show Source): You can put this solution on YOUR website!

24 =
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
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Answer: 30 two digit numbers are relatively prime to 24
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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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