Discussion

Explanation:

For a number n = a^x × b^y × c^z

Sum of co-primes of n, less than n is = $\frac{\mathrm{n}}{2}\times \mathrm{n}\left(1-\frac{1}{\mathrm{a}}\right)\left(1-\frac{1}{\mathrm{b}}\right)\left(1-\frac{1}{\mathrm{b}}\right)$

36 = 2² × 3²

∴ The sum of co-primes less than 36 = $\frac{36}{2}\times 36\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)$ = 216.

Note: 1 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 25 + 29 + 31 + 35 = 216.

Hence, 216.

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