Solution a360f8d5-0636-4792-bbe0-cf2aeffd2531

Points: 1 pt

To construct $\operatorname{div}(60)$, we check the quotient and remainder when dividing $60$ by each $i$ from $1$ to $60$.

$i$ | $60/i$ | $R$ | $i$ | $60/i$ | $R$ 

\cellcolor{highlightyellow}$1$ | \cellcolor{highlightyellow}$60$ | \cellcolor{highlightyellow}$0$ | $31$ | $1$ | $29$ 

\cellcolor{highlightyellow}$2$ | \cellcolor{highlightyellow}$30$ | \cellcolor{highlightyellow}$0$ | $32$ | $1$ | $28$ 

\cellcolor{highlightyellow}$3$ | \cellcolor{highlightyellow}$20$ | \cellcolor{highlightyellow}$0$ | $33$ | $1$ | $27$ 

\cellcolor{highlightyellow}$4$ | \cellcolor{highlightyellow}$15$ | \cellcolor{highlightyellow}$0$ | $34$ | $1$ | $26$ 

\cellcolor{highlightyellow}$5$ | \cellcolor{highlightyellow}$12$ | \cellcolor{highlightyellow}$0$ | $35$ | $1$ | $25$ 

\cellcolor{highlightyellow}$6$ | \cellcolor{highlightyellow}$10$ | \cellcolor{highlightyellow}$0$ | $36$ | $1$ | $24$ 

$7$ | $8$ | $4$ | $37$ | $1$ | $23$ 

$8$ | $7$ | $4$ | $38$ | $1$ | $22$ 

$9$ | $6$ | $6$ | $39$ | $1$ | $21$ 

\cellcolor{highlightyellow}$10$ | \cellcolor{highlightyellow}$6$ | \cellcolor{highlightyellow}$0$ | $40$ | $1$ | $20$ 

$11$ | $5$ | $5$ | $41$ | $1$ | $19$ 

\cellcolor{highlightyellow}$12$ | \cellcolor{highlightyellow}$5$ | \cellcolor{highlightyellow}$0$ | $42$ | $1$ | $18$ 

$13$ | $4$ | $8$ | $43$ | $1$ | $17$ 

$14$ | $4$ | $4$ | $44$ | $1$ | $16$ 

\cellcolor{highlightyellow}$15$ | \cellcolor{highlightyellow}$4$ | \cellcolor{highlightyellow}$0$ | $45$ | $1$ | $15$ 

$16$ | $3$ | $12$ | $46$ | $1$ | $14$ 

$17$ | $3$ | $9$ | $47$ | $1$ | $13$ 

$18$ | $3$ | $6$ | $48$ | $1$ | $12$ 

$19$ | $3$ | $3$ | $49$ | $1$ | $11$ 

\cellcolor{highlightyellow}$20$ | \cellcolor{highlightyellow}$3$ | \cellcolor{highlightyellow}$0$ | $50$ | $1$ | $10$ 

$21$ | $2$ | $18$ | $51$ | $1$ | $9$ 

$22$ | $2$ | $16$ | $52$ | $1$ | $8$ 

$23$ | $2$ | $14$ | $53$ | $1$ | $7$ 

$24$ | $2$ | $12$ | $54$ | $1$ | $6$ 

$25$ | $2$ | $10$ | $55$ | $1$ | $5$ 

$26$ | $2$ | $8$ | $56$ | $1$ | $4$ 

$27$ | $2$ | $6$ | $57$ | $1$ | $3$ 

$28$ | $2$ | $4$ | $58$ | $1$ | $2$ 

$29$ | $2$ | $2$ | $59$ | $1$ | $1$ 

\cellcolor{highlightyellow}$30$ | \cellcolor{highlightyellow}$2$ | \cellcolor{highlightyellow}$0$ | \cellcolor{highlightyellow}$60$ | \cellcolor{highlightyellow}$1$ | \cellcolor{highlightyellow}$0$ 

Whenever $R=0$, we include $i$ in $\operatorname{div}(60)$.

Final answer:
\operatorname{div}(60)=\{1,2,3,4,5,6,10,12,15,20,30,60\}