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

Fractions, ratios, percentages, exponents, number patterns, word problems without variables, etc.
zackattack
Posts: 15
Joined: Wed Apr 01, 2009 12:51 pm

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

find a number which will divide into each of the following numbers, leaving the same remainder
723217
480608
508811

stapel_eliz
Posts: 1628
Joined: Mon Dec 08, 2008 4:22 pm
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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!

little_dragon
Posts: 226
Joined: Mon Dec 08, 2008 5:18 pm
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### Re:

If you get the same remainders, then whatever the divisor is must divide the differences!
how do u no?

stapel_eliz
Posts: 1628
Joined: Mon Dec 08, 2008 4:22 pm
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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.

zackattack
Posts: 15
Joined: Wed Apr 01, 2009 12:51 pm

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

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

so ans=79?

nona.m.nona
Posts: 288
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### Re: find a number which will divide into each of the following n

Divide each number by 79, and see what you get.

zackattack
Posts: 15
Joined: Wed Apr 01, 2009 12:51 pm

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

i got rmndr 51 thnx!!!