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

[zackattack]

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

[stapel_eliz]

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]

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

how do u no?

[stapel_eliz]

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!

[zackattack]

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]

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

[zackattack]

i got rmndr 51 thnx!!!