HCF & LCM · Basic Numeracy · UPSC Civil Service

A 4-digit number $N$ is such that when divided by $3,5,6$, 9 leaves a remainder $1,3,4,7$ respectively. What is the smallest value of $\mathbf{N}$ ?

There are $n$ sets of numbers each having only three positive integers with LCM equal to 1001 and HCF equal to 1 . What is the value of $n$ ?

Let $P=Q Q Q$ be a 3-digit number. What is the HCF of P and 481 ?

How many consecutive zeros are there at the end of the integer obtained in the product $1^2 \times 2^4 \times 3^6 \times 4^8 \times \ldots \times 25^{50}$?

421 and 427, when divided by the same number, leave the same remainder 1. How many numbers can be used as the divisor in order to get the same remainder 1?

A can X contains 399 litres of petrol and a can Y contains 532 litres of diesel. They are to be bottled in bottles of equal size so that whole of petrol and diesel would be separately bottled. The bottle capacity in terms of litres is an integer. How many different bottle sizes are possible?