List of top Mathematics Questions on Divisibility and Remainder

The number of 3-digit integers that are multiple of 6 which can be formed by using the digits 1, 2, 3, 4, 5, 6 without repetition is:
LCM of 9, 12 and 15 is?
If \( x, y \) and \( z \) are distinct prime numbers, then the H.C.F. of \( x^2 y^3 z \) and \( x^3 y z^2 \) is:
Among the given numbers below, the smallest number which will be divided by 9, 10, 15 and 20 and leaves the remainders 4, 5, 10 and 15, respectively, is:
The remainder when the square of any prime number greater than 3 is divided by 6 is

Let the number  \((22)^{2022}\) + \((2022)^{22}\)  leave the remainder \( \alpha \) when divided by 3 and \( \beta \) when divided by 7. Then \( (\alpha^2 + \beta^2) \) is equal to:}

The greatest number which on dividing 1657 and 2037 leaves remainders 6 and 5 respectively is
If log \(\frac{a}{b}\)+log \(\frac{a}{b}\) log (a+b) , then
According to the fundamental theorem of arithmetic, if p (a prime number) divides a2, a is +ve integer, then
If p and q are two positive integers such that p= a3 b2 and q = ab3, where a and b are prime numbers, then HCF (p, q) is
If A = {1, 2, 3, 4, 5) and B = {4, 5, 6, 7}, then A- B=
If the characteristic of logarithm of a number is n, then the number of digits in the number is
Which one of the following statements is true?
The smallest number which leaves remainders 8 and 12 when divided by 28 and 32 respectively is
Sum of the squares of two consecutive even positive integers is 340. The numbers are
Let \( n \) be a 5-digit number and let \( q \) and \( r \) be the quotient and remainder respectively, when \( n \) is divided by 100. For how many values of \( n \) is \( q + r \) divisible by 11?
For all \( n \in \mathbb{N}, 72n - 48n - 1 \) is divisible by