The set of the odd divisors of 72 is ____.

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Detailed Solution

Concept- The set of the odd divisors of 72 is 1,3,9.
By identifying all the integers from 1 to 72 that divide 72, it is possible to determine all the factors of the number 72. Alternately, take 72 and subtract all powers of two to determine its divisors. Explain why the new number's divisors will all be odd and why the group of them will also include all the odd divisors of 72.
A number is said to be a divisor of another number if and only if there is an integer k such that when that number is divided, the result is b = ak. The mathematical symbol for "a divides b" is a|b.
1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72 all divide into 72.
The odd divisors among them are 3 and 9.
Thus, 1,3,9 is the set of odd divisors of 72.
Note: As an alternative, there is
72=2332 the divisors of 32 will be the odd divisors of 72.
Also, odd divisors do not have any power of 2.
The set of odd divisors of 72 and the set of divisors 32will be the same.
Now the set of divisors of 32 is {1,3,9}
Hence, the set of odd divisors of 72 is {1,3,9}.

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