what is the sum of all even factors of 1000?


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Question Number 181275 by Linton last updated on 23/Nov/22

$w h a t i s t h e s u m o f a l l$ $e v e n f a c t o r s o f 1000 ?$
Commented by Rasheed.Sindhi last updated on 24/Nov/22
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Commented by Linton last updated on 24/Nov/22

$w e l l d o n e$
Commented by Acem last updated on 24/Nov/22

$♡ ♡$
Commented by Frix last updated on 23/Nov/22

$1000 = 2^{3} 5^{3}$ $sum of even factors is$ $(1 + 5 + 5^{2} + 5^{3}) (2 + 2^{2} + 2^{3}) = 2184$
Commented by Rasheed.Sindhi last updated on 23/Nov/22

$S i r t h i s i s a c o m p l e t e s o l u t i o n,$ $m o r e t h a n a c o m m e n t!$
Commented by Frix last updated on 23/Nov/22

$I^{'} ve been afraid others might claim it is$ $n o t a complete solution because I {didn}^{'} t$ $explain it . . .$
Commented by Acem last updated on 23/Nov/22

$@ S i r R a s h e e d, H a v e a g o o d e v e n i n g b r o .$
	Answered by Acem last updated on 23/Nov/22

	$e v e n \times o d d = e v e n$ $t h e 1000 = 2^{3} 5^{3}$ $2^{i} 5^{j} \forall i : 2^{i} i s e v e n, \forall j : 5^{j} i s o d d$ $T h e r e q u e s t i s t h e s u m o f t h e e v e n f a c t o r s o f 1000$ $S u m = \underset{i = 1}{\sum^{3}} 2^{i} \underset{j = 0}{\sum^{3}} 5^{j} t h a t m e a n s w e h a v e 12 n u m b e r s$ $S u m = 14 \times 156 = 2 184$ ${I t}^{'} s f u n n y a p p e a r i n g t h e q u e s t i o n 1 0 0 0$
	Commented by Rasheed.Sindhi last updated on 24/Nov/22

	$I s t h e f o l l o w i n g c o r r e c t ? :$ $S u m o f e v e n f a c t o r s o f 1000$ $= 2 \times S u m o f a l l f a c t o r s o f 500$
	Commented by Linton last updated on 24/Nov/22

	$w e l l d o n e$
	Commented by Rasheed.Sindhi last updated on 24/Nov/22

	$@ A c e m, I a l s o t h i n k s o .$
	Commented by Acem last updated on 24/Nov/22

	$I t h i n k y e s, b e c a u s e e i t h e r i t f a c t o r s w e r e e v e n$ $o r o d d t h e r e s u l t a f t e r m u l t i p l y i n g t h e m b y 2$ $w i l l b e e v e n, r i g h t ?$
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