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Find the sum of the multiples of 19 or 5 under 775

Guest May 25, 2017

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 #2
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The number of multiples of 19 < 775  =  775 / 19  =  40

 

And their sum  =   19 (40)(41)/2  = 15580

 

The number of multiples of 5 < 775  =  770 / 5 =   154

 

And their sum  =  5 (154)(155) / 2  =  59675

 

However....we must subtract out the sum of all numbers divisible by both 5 and 19.......this will equal all the multiples  of 19 * 5  = 95.......so  775/95  =  8

 

So...the sum of these  = 95 (8) (9)/2  =  3420

 

So...the total sum of all multiples of 5 or 16 less than 775  =  [ 15580 + 59675 - 3420 ]  = 71835

 

 

cool  cool  cool

CPhill  May 25, 2017
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 #1
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Find the sum of the multiples of 19 or 5 under 775.

 

Well, the easiest way to do it is as follows:

775 / 19 =40.7894....... Just drop the fraction and keep 40. That means there are 40 multiples of 19 up to 775.

Now, you can use an Arithmetic Progression to add them up:

Sum =n/2[2a + (n - 1)d] =40/2[2*19 + (40 - 1)*19] =20[38 + 741] =15,580 - which is the total of all multiples of 19 up to 775.

 

Now, do exactly the same thing with 5 =775 / 5 =155. This is how many multiples of 5 you have up to 775.

Use the same formula as above to add them all up. If you do it right, you should get a total of =60,450. Now, try to see if you get the same number. Good luck.

Guest May 25, 2017
edited by Guest  May 25, 2017
 #2
avatar+75344 
+1
Best Answer

 

The number of multiples of 19 < 775  =  775 / 19  =  40

 

And their sum  =   19 (40)(41)/2  = 15580

 

The number of multiples of 5 < 775  =  770 / 5 =   154

 

And their sum  =  5 (154)(155) / 2  =  59675

 

However....we must subtract out the sum of all numbers divisible by both 5 and 19.......this will equal all the multiples  of 19 * 5  = 95.......so  775/95  =  8

 

So...the sum of these  = 95 (8) (9)/2  =  3420

 

So...the total sum of all multiples of 5 or 16 less than 775  =  [ 15580 + 59675 - 3420 ]  = 71835

 

 

cool  cool  cool

CPhill  May 25, 2017

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