find a number which will divide into each of the following n  TOPIC_SOLVED

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find a number which will divide into each of the following n

Postby zackattack on Sat Aug 01, 2009 5:20 pm

find a number which will divide into each of the following numbers, leaving the same remainder
723217
480608
508811
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Postby stapel_eliz on Sat Aug 01, 2009 7:06 pm

Hint: Try finding the prime factorizations of each difference between pairs of numbers. If you get the same remainders, then whatever the divisor is must divide the differences! :wink:
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Re:

Postby little_dragon on Wed Aug 05, 2009 7:36 pm

stapel_eliz wrote:If you get the same remainders, then whatever the divisor is must divide the differences!

how do u no?
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Postby stapel_eliz on Wed Aug 05, 2009 9:08 pm

little_dragon wrote:how do u no?

Let the original numbers be "a" and "b", the divisor be "d", and the equal remainder be "r". Then, by definition of division, etc, we get:

a = md + r

b = nd + r

(The "m" and "n" will be the answers across the top of the long division, the part that "d" went "evenly" into. This is like "thirteen divided by four has a remainder of one" can also be written as "13 = 3*4 + 1".)

The difference then is:

(md + r) - (nd + r) = md - nd = (m - n)d

So the divisor must divide the differences.

Hope that made sense! :wink:
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Re: find a number which will divide into each of the following n

Postby zackattack on Thu Aug 06, 2009 11:04 pm

723217-480608=242609=37*79*83
723217-508811=214406=2*23*59*79
508811-480608=28203=3*7*17*79

so ans=79?
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Re: find a number which will divide into each of the following n  TOPIC_SOLVED

Postby nona.m.nona on Sun Aug 09, 2009 8:41 pm

Divide each number by 79, and see what you get.
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Re: find a number which will divide into each of the following n

Postby zackattack on Sat Aug 15, 2009 1:37 pm

i got rmndr 51 thnx!!!
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