# 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.

 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 < 18So, 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.

 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.

 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).