Question

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

Answer 1

On prime factorization, we find that 181 is a prime number.


Hence, to find the smallest natural number to be added to 1024 to get a multiple of 181, we will find the multiple of 181 closest to 1024.

we have,
$181\ast 5=905$
$181\ast 6=1086$
$181\ast 7=1267$
We see that 1086 is closest to 1024.
1086 - 1024 = 62
Hence, the smallest natural number to be added to 1024 to get a multiple of 181 is 62.