# Divisibility

### 5^6 - 1 is divisible by

56 - 1 is divisible by

1. 5
2. 13
3. 31
4. None of these

### If n is any odd number greater than 1, then n(n^2 - 1) is

If n is any odd number greater than 1, then n(n2 - 1) is

1. divisible by 24 always
2. divisible by 96 always
3. divisible by 48 always
4. None of these

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

Let N = 553 + 173 - 723. N is divisible by

1. both 3 and 17
2. both 7 and 13
3. both 3 and 13
4. both 17 and 7

### What will be remainder when (67^67 + 67) is divided by 68

What will be remainder when (6767 + 67) is divided by 68?

1. 67
2. 63
3. 66
4. 1

### Find the minimum integral value of n such that the division

Find the minimum integral value of n such that the division 55n/124 leaves no remainder

1. 124
2. 123
3. 31
4. 62

### Let k be a positive integer such that k+4 is divisible by 7

Let k be a positive integer such that k+4 is divisible by 7. Then the smallest positive integer n, greater than 2, such that k+2n is divisible by 7 equals

1. 7
2. 5
3. 9
4. 3

### Let p be a prime number greater than 5. Then (p^2 - 1) is

A positive integer is said to be a prime number if it is not divisible by any positive integer other than itself and 1. Let p be a prime number greater than 5. Then (p2 - 1) is

1. always divisible by 6, and may or may not be divisible by 12
2. always divisible by 24
3. never divisible by 6
4. always divisible by 12, and may or may not be divisible by 24