What is the least natural number you have to add to 1024 to get a multiple of 181?

Answer 1

Apply Euclid's Division Lemma(or in simple words Division Algorithm) to 1024 and 181:

1024 = 181 x 5 + 119

181 goes 5 times into 1024 with remainder 119.

It means if we subtract 1024 from the 6th multiple of 181 then we get the required which is to be added to 1024.

Way of obtaining 6th multiple:

(This method is useful when we deal with large numbers!)

If we subtract 119 from 1024 then we get 5th multiple of 181.

1024 - 119 = 905. And on adding 181 to 905 we get the 6th multiple of 181.

181 + 905 = 1086.

And 1086 - 1024 = 64 is the required number.

Answer 2

62 is the answer...