Name: Properties of Division of Integers
Uploaded: 2019-07-19
Duration: 8 min 15 s
Description: Learn everything you'll need to know about the properties of the division of integers in a quick and short lesson that'll help you master the concept.

Question

Complete the magic square so that the product of the integers in each row, column or diagonal is $- 46656$ .

$72$
	$- 36$
$- 12$

Accepted Answer

Given,

To complete the magic square so that the product of the integers in each row, column or diagonal is $- 46656$

Let,

$72$ $b$ $- 36$

$a$ $- 12$ $d$

$- 12$ $f$ $e$

First, complete the first column

$72 \times (a) \times (- 12) = - 46656$

$- 864 a = - 46656$

$a = \frac{- 46656}{- 864} = 54$

Now complete the second row,

$54 \times (- 36) \times d = - 46656$

$- 1944 d = - 46656$

$d = \frac{- 46656}{- 1944} = 24$

Now complete both the digonals,

$- 12 \times - 36 \times c = - 46656$

$432 c = - 46656$

$c = \frac{- 46656}{432} = - 108$

now, $72 \times - 36 \times e = - 46656$

$- 2592 e = - 46656$

$e = \frac{- 46656}{- 2592} = 18$

Now complete the third row,

$- 12 \times f \times 18 = - 46656$

$- 216 f = - 46656$

$f = \frac{- 46656}{- 216} = 216$

Now complete the second column,

$b \times - 36 \times 216 = - 46656$

$- 7776 b = - 46656$

$b = \frac{- 46656}{- 7776} = 6$

Now complete the first row,

$72 \times 6 \times c = - 46656$

$432 c = - 46656$

$c = \frac{- 46656}{432} = - 108$

Now we can complete all the rows.

$72$ $6$ $- 108$

$54$ $- 36$ $24$

$- 12$ $216$ $18$

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