20+ CAT Remainders Questions With Video Solution & Formulas

How many of the integers 1, 2, … , 120, are divisible by none of 2, 5 and 7?

The number of integers x such that $$0.25 \leq 2^x \leq 200$$ and $$2^x + 2$$ is perfectly divisible by either 3 or 4, is

Let $$n!=1*2*3* ...*n$$ for integer $$n \geq 1$$.

If $$p = 1!+(2*2!)+(3*3!)+... +(10*10!)$$, then $$p+2$$ when divided by 11! leaves a remainder of

If x = $$(16^3 + 17^3+ 18^3+ 19^3 )$$, then x divided by 70 leaves a remainder of

The remainder, when $$(15^{23} + 23^{23})$$ is divided by 19, is

How many even integers n, where $$100 \leq n \leq 200$$ , are divisible neither by seven nor by nine?

The number of positive integers n in the range $$12 \leq n \leq 40$$ such that the product (n -1)*(n - 2)*…*3*2*1 is not divisible by n is

When $$2^{256}$$ is divided by 17, the remainder would be

After the division of a number successively by 3, 4 and 7, the remainders obtained are 2, 1 and 4 respectively. What will be the remainder if 84 divides the same number?

$$7^{6n} - 6^{6n}$$, where n is an integer > 0, is divisible by

Let $$b$$ be a positive integer and $$a = b^2 - b$$. If $$b \geq 4$$ , then $$a^2 - 2a$$ is divisible by

Let n be the number of different five-digit numbers, divisible by 4 with the digits 1, 2, 3, 4, 5 and 6, no digit being repeated in the numbers. What is the value of n?

Let N = 1421 * 1423 * 1425. What is the remainder when N is divided by 12?

The integers 34041 and 32506 when divided by a three-digit integer n leave the same remainder. What is n?

Let N = $$55^3 + 17^3 - 72^3$$. N is divisible by:

The remainder when $$7^{84}$$ is divided by $$342$$ is :

A certain number, when divided by 899, leaves a remainder 63. Find the remainder when the same number is divided by 29.

A number is formed by writing first 54 natural numbers next to each other as 12345678910111213 ... Find the remainder when this number is divided by 8.

If m and n are integers divisible by 5, which of the following is not necessarily true?

Find the minimum integral value of n such that the division $$\frac{55n}{124}$$ leaves no remainder.