Theory of Numbe...

What is the highest factor of 1573, except the number itself?

Find the last digit of (173)⁹⁹.

What is the rightmost non-zero digit of 270²⁷⁰ + 130¹³⁰?

What is the last digit of the result, if 6⁶³ is divided by 4²³?

The smallest positive number which leaves remainder 1 when divided by 3, 4, 5 or 7 is

Find the numbers between 400 and 550, which when divided by 6, 8, or 9, leave 5 as the remainder in each case.

x and y are distinct two-digit numbers. If their HCF is 14, what is the maximum possible value of x + y?

Find the number of factors of 5005.

How many factors of 1440 are perfect squares?

How many numbers divisible by each of the numbers 21, 36 and 66 are there such that they are less than 10,000?

M and N are two distinct natural numbers. The HCF and LCM of M and N are K and L, respectively. If A is also a natural number, then which of the following relations is not possible?

If HCF of 8 numbers has to be found by the division method, then how many steps would be required?

Which least number must be subtracted from 1856, so that the remainder is 4 when divided by 7, 12, 16?

Express the sum of repeating decimals and as a repeating decimal.

Find the value of

x = 0.ababab…… and y = 0.baaa…….. If x = y, then what is the relation between a and b?

If N = 1000⁸ - 8, what is the sum of its digits?

If x = – 0.25, which of the following is the greatest?

If 2^{x + y} = 4^{x – y}, then 3^x/y is

If ´ = 1. What is the value of x?