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Direct Proportion

Find number o...

Question

Find number of divisors of $1980 .$
$(i)$ How many of them are multiple of $11 ?$ find their sum.

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Solution

divisors of $1980$ are

$1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 15, 18, 20, 22, 30, 33, 36, 44, 45, 55, 60, 66, 90, 99, 110, 132, 165, 180,$

$198, 220, 330, 396, 495, 990, 1980$

Number of divisors is $35$

$i)$ Number of multiples of $11$ are $17$

$S u m = 11 (1 + 2 + 3 + 4 + 5 + 6 + 9 + 10 + 11 + 12 + 15 + 18 + 20 + 22 + 30 + 33 + 36 + 44 + 55 + 60 + 66 +$ $90 + 99 + 110 + 132 + 165 + 180) = 13618$

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