A positive number has 8 distinct divisors Lets say a, b, c, d, e, f, g and h Given a . b . c . d . e . f . g . h = 3111696 Find that number


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Question Number 27651 by Joel578 last updated on 12/Jan/18

$A positive number has 8 distinct divisors$ $Lets say a, b, c, d, e, f, g and h$ $Given a . b . c . d . e . f . g . h = 3111696$ $Find that number$
Commented by Joel578 last updated on 12/Jan/18

$What is distinct divisor ? Can we say that is$ $it same as factor ?$
Commented by Rasheed.Sindhi last updated on 14/Jan/18

$Distinct divisors means differnt$ $divisors and yes divisor is same$ $as factor .$ $If a ∣ c & b ∣ c & a \neq b then a and b$ $are distinct divisors .$
	Answered by mrW2 last updated on 14/Jan/18

	$T h e n u m b e r i s 2 \times 3 \times 7 = 42 . I t h a s$ $e x a c t l y 8 (d i s t i n c t) d i v i s o r s :$ $1 (= a)$ $2 (= b)$ $3 (= c)$ $6 (= d)$ $7 (= e)$ $14 (= f)$ $21 (= g)$ $42 (= h)$ $T h e p r o d u c t o f a l l t h o s e d i v i s o r s i s$ $a \cdot b \cdot c \cdot d \cdot e \cdot f \cdot g \cdot h = 1 \times 2 \times 3 \times 6 \times 7 \times 14 \times 21 \times 42 = 311696$
	Commented by Rasheed.Sindhi last updated on 13/Jan/18

	$Hi Sir mrW 1 ∣ mrW 2$ $Your answer is perfect as it contains$ $all the divisors of required number .$ $I deleted my answer because its$ $logic was deffective .$
	Commented by mrW2 last updated on 13/Jan/18

	$S i r, t o b e h o n e s t, I {d i d n}^{'} t c a t c h t h e$ $q u e s t i o n r e a l l y t i l l I s a w y o u r w o r k i n g .$ $I t b r o u g h t m e f i n a l l y t o t h e r i g h t$ $u n d e r s t a n d i n g a n d t o t h e a n s w e r .$ $T h e r e f o r e t h a n k y o u f o r y o u r w o r k i n g!$
	Commented by Rasheed.Sindhi last updated on 13/Jan/18

	$T h A n K s S i R!$ $C ould Y ou H elp M e in solving$ $You can't use 'macro parameter character #' in math mode$
	Answered by mrW2 last updated on 14/Jan/18

	$A n o t h e r w a y t o s o l v e t h i s q u e s t i o n :$ $W e k n o w t h e n u m b e r, {l e t}^{'} s s a y N h a s$ $8 d i f f e r e n t d i v i s o r s a, b, c . . ., h .$ $W e k n o w i f n u m b e r k i s a d i v i s o r o f$ $N, t h e n \frac{N}{k} m u s t b e a n o t h e r d i v i s o r o f$ $i t, t h e p r o d u c t o f b o t h d i v i s o r s i s N .$ $T h i s i s t o s a y i f w e a r r a n g e a, b, c . . ., h$ $i n c r e a s i n g l y, {w e}^{'} l l h a v e$ $a \cdot h = N$ $b \cdot g = N$ $c \cdot f = N$ $d \cdot e = N$ $T h e n {w e}^{'} l l g e t$ $a \cdot b \cdot c \cdot d \cdot e \cdot f \cdot g \cdot h = N^{4} = 3111696 (a s g i v e n)$ $a c c o r d i n g t o S i r R a s h e e d . S i n d h i : 3111696 = {(2 \times 3 \times 7)}^{4}$ $\Rightarrow N = 2 \times 3 \times 7 = 42$
	Commented by Rasheed.Sindhi last updated on 14/Jan/18

	$C r e a t i v e w o r k S i r!$ $T h i s i s r e a l y a^{'} m e t h o d^{'} f o r$ $s u c h p r o b l e m s!$
	Commented by Joel578 last updated on 14/Jan/18

	$t h a n k y o u v e r y m u c h$
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