Divisibility Rule for Composite Numbers

Q. What is the remainder when $(1!{)}^3+(2!{)}^3+(3!{)}^3+(4!{)}^3+\dots \dots (1152!{)}^3$ is divided by 1152?

1. 225
2. 205
3. 325
4. 125

Q. The least possible number with which (180)! should be multiplied so that it can be divided by $(45{)}^{44}$ is:

1. 44
2. none of these
3. 25
4. 9

Q. The greatest possible divisor of $3^{2n+3}$ - 24n - 27 for every n $ϵ$ N, which necessarily divides is:

1. 24
2. 96
3. 64
4. None of these

Q. When a number is divided by 3, 4, and 7 successively, remainders obtained are 2, 1, and 4 respectively. What will be the remainder when the same number is divided by 84?

1. 53
2. 63
3. 73
4. 43

Q. Find the remainder when $({10}^3+9^3{)}^{752}$ is divided by ${12}^3$.

1. 729
2. 1000
3. 752
4. 1

Q. What will be the value of remainder when (111111111 ..... 64 terms) $\times$ (22222222 ........ 55 terms) is divided by 18?

1. 1
2. 0
3. 2
4. 17

Q. What is the remainder when $2(8!)-21(6!)$ divides $14(7!)+14(13!)$?

1. 9!
2. 1
3. 7!
4. 8!

Q. What is the digit at the hundredths place of the number $(225{)}^{40}$?

1. 6
2. 2
3. 4
4. 8

Q. Find the remainder when $7^{99}$ is divided by 2400.

1. 1
2. 343
3. 49
4. 7

Q. What is the remainder when ${128}^{1000}$ is divided by 153?

1. 118
2. 145
3. 103
4. 52