Finding divisors systematically

#divisors#enumeration#bounds

Statement

Find all positive divisors of $20$ .

Hint

If $d\mid20$ and $d>0$ , then $d\le20$ . Test $d=1,\ldots,20$ , or use $20=2^2\cdot5$ .

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Factorization. $20=2^2\cdot5$ . The divisors are $2^a5^b$ with $0\le a\le2$ , $0\le b\le1$ :
$1,2,4,5,10,20.$

Verification. $20=1\cdot20=2\cdot10=4\cdot5$ .