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Similar to this question: How to divide a number by $2$ numbers?

I would like to know how to divide a number (let's say 23) by two different numbers (say, 1.6 and 2.4) to find what combination of the two different numbers makes up exactly 23 - or find out the remainder after reaching the closest number.

Unlike the linked question, I cannot guarantee that the number (23 here) is divisible by any combination of the two different numbers; on top of this I would like to find the most balanced combination of the two different numbers (such as 1.6*5 and 2.4*4 as opposed to 1.6*17 and 2.4*2, just pulling numbers out of thin air to explain the point here).

I'm sure this is a simple question, but I don't know where to start...

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  • Well, the definition of divisibility and remainders go out of the window when you take rationals instead of integers. – SS_C4 May 01 '16 at 15:50
  • Ah okay, well if you feel anything about my question ought to be changed feel free to make suggestions or use the built in "edit" functionality. – Unencoded May 01 '16 at 16:39
  • Alright. Here you have taken the number 23. Is that number supposed to be rational or integer? Similarly for the numbers that divide it. Are they rationals or irrationals? – SS_C4 May 02 '16 at 01:06
  • All rational numbers, perhaps it would be better to work with money as the context here: £23 divided by combinations of £1.60 and £2.40. I'm afraid I won't be around for a few hours now, but thank you for any help you can offer. – Unencoded May 02 '16 at 01:17

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