Question

what least number should be added to 27885 so that the sum is exactly divided by 58 ?​

Answer 1

Step by step explanation:-

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What least number should be added to 27,835 so that the sum is exactly divided by 56?

So, we are looking for an integer n such that 27835 + n = 56 m, where m is also an integer.

Note that 27 835 = 28 000 - 165 = 28 000 - 168 + 3 = 56 (500 - 3) + 3 = 56 (497) + 3

Thus we have: 56 (487) + 3 + n = 56 m

We need to find the smallest value of n such that 3 + n is a multiple of 56.

Well, looking at this, the obvious answer is n = 56 - 3 = 53.

But this is only correct is we restrict n to being a positive integer. There is nothing in the question that leads us to assume this to be the case, so we’ll free to consider negative values of n.

Consider n = -3; I’m sure you will agree that -3 < 53, as for our second requirement, 27835 + -3 = 56 (487) + 3 - 3 = 56 (487), which is clearly a multiple of 56.

But I can find a smaller number than -3; consider -563.

But I’m done done yet. Consider -560 000 003

There is no minimum value of n.

I hope my answer is helpful for you ✌️☺️