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\\February 27, 2024 10:04 AM Surender Prajapati Proof 5 Reader _________________________ Date: ___________________74

example 2: Find the quotient and remainder for the following and check the answer.
(a) 504084 ÷ 6 (b) 621575 ÷ 25

Solution: 8 4 0 1 4 Q Step 1: Since 5 < 6, we divide 2-digit number 50 by 6.
(a) 6 5 0 4 0 8 4 6 × 8 = 48 is the maximum possible product
– 4 8 obtained < 50. Subtract 48 from 50 and bring
2 4 down 4.
– 2 4
0 8 Step 2: 24 is the new dividend. Here, 6 × 4 = 24 is the
– 6 maximum possible product obtained.
2 4 Subtract 24 from 24 and bring down 0.
– 2 4
0 R Step 3: Since 0 < 6, put 0 in quotient and bring down 8.
Now, 08 is the new partial dividend. Here, 6 × 1 =
6 is the maximum possible product < 8. Subtract
6 from 8 and bring down 4.
Step 4: 24 is the new dividend. Here, 6 × 4 = 24. Now,
nothing is left and no number is left to bring

down. So, stop.
Checking: Thus, Quotient = 84014 and Remainder = 0

Quotient × Divisor + Remainder = Dividend
84014 × 6 + 0 = 504084 + 0 = 504084. The division is correct.

(b) 2 4 8 6 3 Q Step 1: 62 > 25. So, divide 62 by 25. 25 × 2 = 50 is the
25 6 2 1 5 7 5 maximum possible product obtained < 62.
– 5 0 Subtract 50 from 62 and bring down 1.

1 2 1 Step 2: 121 is the new dividend. Here, 25 × 4 = 100 is
– 1 0 0 the maximum possible product obtained < 121.
2 1 5 Subtract 100 from 121 and bring down 5.
– 2 0 0 Step 3: 215 is the new partial dividend. Here, 25 × 8 =

1 5 7 200 is the maximum possible product < 215.
– 1 5 0 Subtract 200 from 215 and bring down 7.
7 5
– 7 5 Step 4: 157 is the new dividend. Here, 25 × 6 = 150 < 157.
0 R Subtract 150 from 157 and bring down 5.
Step 5: 75 is the new dividend. Here, 25 × 3 = 75 = 75.

Subtract 75 from 75. Nothing is left and no
number is left to bring down.
Thus, Quotient = 24863 and Remainder = 0
Checking:
Quotient × Divisor + Remainder = Dividend

24863 × 25 + 0 = 621575 + 0 = 621575. The division is correct.

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