# Remainders

### After the division of a number successively by 3, 4 and 7, the remainders

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?

1. 53
2. 75
3. 41
4. 80

### When 2^256 is divided by 17, the remainder would be

When 2256 is divided by 17, the remainder would be

1. 1
2. 14
3. 16
4. None of these

### 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 N = 1421 × 1423 × 1425. What is the remainder when N is divided by 12

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

1. 0
2. 9
3. 6
4. 3

### On dividing a number by 5, we get 3 as remainder

On dividing a number by 5, we get 3 as remainder. What will the remainder when the square of the this number is divided by 5?

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

### What is the sum of all two-digit numbers that give a remainder of 3

What is the sum of all two-digit numbers that give a remainder of 3 when they are divided by 7?

1. 676
2. 777
3. 683
4. 666

### The remainder obtained when a prime number greater than 6 is divided by 6 is

The remainder obtained when a prime number greater than 6 is divided by 6 is

1. 1 or 3
2. 1 or 5
3. 3 or 5
4. 4 or 5

### The remainder when 7^84 is divided by 342 is

The remainder when 784 is divided by 342 is

1. 0
2. 1
3. 49
4. 341

### The smallest number which when divided by 4, 6 or 7 leaves a remainder of 2, is

The smallest number which when divided by 4, 6 or 7 leaves a remainder of 2, is

1. 86
2. 80
3. 62
4. 44

### What is the remainder when 4^96 is divided by 6

What is the remainder when 496 is divided by 6?

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

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

If x = (163 + 173 + 183 + 193), then x divided by 70 leaves a remainder of

1. 0
2. 1
3. 35
4. 69

### Which is the least number that must be subtracted from 1856

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

1. 137
2. 140
3. 172
4. 1361