Divide by 2-digit Divisors

We will learn step-by-step how to divide by 2-digit divisors.

Let us consider some examples of division by two-digit numbers or divisors.

1. Divide 618 by 12.

Divide 618 by 12

Quotient = 51

Remainder = 6

Divisor (12) has two digits. Consider the two digits of the dividend from the left (61).

Now, consider the left most digit of the divisor 12 i.e. 1 and the left most digit of the dividend i.e. 6.

As, 1 goes into 6, 6 times. So, 6 may be the left most digit of the quotient.

Let us check 12 × 6 = 72, but 72 > 61.

Now, consider 5 instead of 6 as left most digit of the quotient.

Let us check 12 × 5 = 60, but 60 < 61.

Now, write 5 as the left most digit of the quotient and 60 below the 61.

Subtract 61 - 60 = 1. Write 1 as remainder.

Bring down 8 from the dividend 618 and write it to the right of 1.

It makes the remainder 18, which we consider as dividend now. i.e. we have to find 18 ÷ 12.

1 goes into 1, 1 time. So, 1 may be the second digit of the quotient.

Let us check. 12 × 1 = 12 and 12 < 18

So, write 1 as quotient next to the 5 and 12 below the 18.

Subtract 18 - 12 = 6. Write 6 as remainder.

6 becomes the final remainder as there is no digit left in dividend 618 to bring down and the remainder 6 cannot be divided by the divisor 12.


 2. Divide 8268 by 15.

Divide 8268 by 15

Quotient = 551

Remainder = 3

Divisor (15) has two digits. So, we will divide by 2-digit divisors. Consider the two digits of the dividend from the left (82).

Now, consider the left most digit of the divisor 15 i.e. 1 and the left most digit of the dividend i.e. 8.

As, 1 goes into 8, 8 times. So, 8 may be the left most digit of the quotient.

Let us check 15 × 8 = 120, but 120 > 82.

So, consider 7 and check 15 × 7 = 105, but 105 > 82.

Now, consider 6 and check 15 × 6 = 90, but 90 > 82.

Now, consider 5 and check 15 × 5 = 75, and 75 < 82.

Write 5 as the left most digit of the quotient and 75 below the 82.

Subtract 82 - 75 = 7. Write 7 as remainder.

Bring down 6 from the dividend 8268 and write it to the right of 7.

It makes the remainder 76, which we consider as dividend now. i.e. we have to find 76 ÷ 15.

Repeat the process of 2nd step till we get a remainder either 0 or a number which is not divisible by divisor (15).


3. Divide 4573 by 52.

Divide 4573 by 52

Quotient = 87

Remainder = 49

Divisor (52) has two digits. So, we will divide by 2-digit divisors. Consider the two left most digits of the dividend (45).

Since 45 < 52. Consider 3 left most digits of dividend i.e. 457. Because 1st digit of divisor (5) is greater than 1st digit of dividend (4) so, consider 45.

5 goes into 45, 9 times. So, 9 may be the left most digit of the quotient.

Let us check 52 × 9 = 468, but 468 > 457.

Consider 8 and check 52 × 8 = 416, but 416 < 457.

Write 8 as quotient and 416 below the 457.

Subtract 457 - 416 = 41. Write 41 as remainder.

Bring down 3 from the dividend 4573 and write it to the right of 41.

Consider 413 as dividend now. i.e. we have to find 413 ÷ 52.

Repeat the process of 2nd step till we get a remainder either 0 or a number which is not divisible by divisor (52).





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