Identify the Practical Number
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30
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22
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44
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54
A practical number is a positive integer n where every positive integer ≤ n can be written as a sum of distinct divisors of n. For 30, divisors are 1,2,3,5,6,10,15,30 and all numbers 1-30 can be formed. For 54, divisors are 1,2,3,6,9,18,27,54 and all numbers 1-54 can be formed. 22 and 44 are not practical numbers - they cannot represent all smaller integers.
A practical number is one where every smaller positive integer can be written as a sum of its distinct divisors. 30 (divisors 1,2,3,5,6,10,15) and 54 (divisors 1,2,3,6,9,18,27) both satisfy this. 22 and 44 fail because their divisor sums are too small relative to the number (e.g., 22's proper divisors 1+2+11=14 can't reach values like 21), making them deficient rather than practical.