Remainders and Successive division - Quant Study Notes for Competitive Exams

What is the remainder?

If we divide some number (say a) with another number (say b), there were only two cases: i) It will fully divide the number, or ii) It will not fully divide the number. In the second case, it leaves a number (say r), and the significance of this number is, if we subtract this number from the original number, then that (a – r) will be divisible by b. So, this r is called remainder.

Find quotient and remainder if 684 is divided by 7.

684 = 7 × 97 + 5 Here, the quotient is 97 and the remainder is 5

What is successive division?

If the quotient of a division is taken and this is used as the dividend, such a division is called ”successive division”. This process can continue up to any number of steps – until the quotient in the first division becomes zero or the first time. In easy words, the quotient in the first division is taken as dividend and divided in the second division; the quotient in the second division is taken as the dividend in the third division and so on.

How do you solve successive division?

The quotient in the first division is taken as dividend and divided in the second division; the quotient in the second division is taken as the dividend in the third division and so on

Find the remainder when 7²⁶⁷ is divided by 10.

Sol: Here, we just have to find the last digit of the number. We can see that the last digit of power of 7 starts repeating after every 4th power. So, we can simply divide the power with 4 and find the remainder. So, 267 = 4 × 66 + 3 So, the remainder is 3. Now, the last digit of 7³ is 3. So, the remainder will be 3.