Advanced Same Remain

[noreply]

When 823519 is divided by a number, then the remainder is three times the remainder obtained by dividing 274658 by the same number.

Find the divisor (what you divide with to get the remainders).

[MAS1]

Originally Posted by noreply

When 823519 is divided by a number, then the remainder is three times the remainder obtained by dividing 274658 by the same number.

Find the divisor (what you divide with to get the remainders).

Is there enough info to solve this? It seems like there are 5 variables:

D = divisor
Q1 = quotient 1
Q2 = quotient 2
R1 = remainder 1
R2 = remainder 2

but only 3 equations:


823519 = (Q1)D + R1
274658 = (Q2)D + R2
R1 = 3(R2)

Am I missing something?

[noreply]

I did the problem myself from the start again, and I can finish it.

Clue: You might want to do something to make the remainders the same!

Oh, and also, you shouldn't just try to make equations for problems, sometimes you need to think a bit first.

[MAS1]

The divisor is 91.

274658/91 = 3018 rem 20

823519/91 = 9049 rem 60

I had to use excel and a kind of brute force method to find it. Could you post your method for finding the answer?

Thanks.

[noreply]

Originally Posted by MAS1

The divisor is 91.

274658/91 = 3018 rem 20

823519/91 = 9049 rem 60

I had to use excel and a kind of brute force method to find it. Could you post your method for finding the answer?

Thanks.

Excel is always useful! Although I haven't used excel much, for solving maths stuff, I've seen applications of maths using Excel, and they're quite good.
--------------------------
If the remainder of 823519 is 3 times 274658's remainder, then we can multiply 2746558 by 3, in order to get the same remainder.

274658 * 3 = 823974

Since the remainders of the two numbers are the same, the divisor divides their difference fully. So, you can do:

823974 - 823519 = 455

because the answer will take those remainders away, leaving a number that can be divisible by the divisor.

Then, we find the factors of 455 to see which one is correct - Factors are 5, 7, 15, 35, 65, 91 and 455. Now, there probably is an easier way, but I used trial and error from here on.
I divided both numbers with the divisor and tested to see if it worked out properly.

And, 91 fitted nicely.

[MAS1]

I guess I could have used the equations I had.

Eq. 1: 823519 = (Q1)D + R1
Eq. 2: 274658 = (Q2)D + R2
Eq. 3: R1 = 3(R2)

Substituting Eq.3 into Eq. 1 gives 823519 = (Q1)D + 3(R2)

So we have

(Q1)D + 3(R2) = 823519
(Q2)D + (R2) = 274658

Multiply both sides of the 2nd equation by 3

(Q1)D + 3(R2) = 823519
3(Q2)D + 3(R2) = 823974

Subtracting the equations to eliminate R2 gives

(Q1)D - 3(Q2)D = -455
D((Q1) - 3(Q2) = -455
(Q1) - 3(Q2) = (-455/D)

Then I could have used your method of dividing 455 by its prime factors to find D.

Thanks.

[ahmed]

is it 9109