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\\October 8, 2025 12:09 PM Bharat Arora P-9 Reader _________________________ Date: ___________________74

division of large numbers
Knowledge Desk
Let us recall the terms related to division. The symbol for '÷' called
The number to be divided is called the dividend. 'obelus' was first used

The number by which the dividend is divided is called the in 1659 by the Swiss
mathematician Johann
divisor. Heinrich Rahn in his

The result of division is called the quotient (Q). work– Teutsche Algebra.
When a number is divided by another number and a number
smaller than the divisor is left over, the leftover number is called the remainder (R).
Larger numbers are divided in the same way as smaller numbers.

example 1: Divide 86345 by 23 and check the answer.

Solution: 3 7 5 4 Q Checking:
Divisor 23 8 6 3 4 5 Dividend Quotient × Divisor +
– 6 9 Remainder = Dividend tth th H T O
1 7 3 3 7 5 4
– 1 6 1 3754 × 23 + 3 = 86,345 × 2 3

1 2 4 86,342 + 3 = 86,345 1 1 2 6 2
– 1 1 5 86,345 = 86,345 + 7 5 0 8 0

9 5 The division is correct. 8 6 3 4 2
– 9 2
3 R

example 2: Find the quotient and remainder for the following and check the answer.
( a) 5,04,084 ÷ 6 (b) 6,21,575 ÷ 25

Solution: 8 4 0 1 4 Q Step 1: Since 5 < 6, we divide the 2-digit number 50 by 6. 6 × 8
( a) 6 5 0 4 0 8 4 = 48 is the maximum possible product < 50.
– 4 8 Subtract 48 from 50 and bring down 4.
2 4
– 2 4 Step 2: 24 is the new partial dividend. Here, 6 × 4 = 24 is
0 8 the maximum possible product obtained.
– 6 Subtract 24 from 24 and bring down 0.
2 4 Step 3: Since 0 < 6, put 0 in the quotient and bring down
– 2 4 8. Now, 08 is the new partial dividend. Here, 6 × 1
0 R
= 6 is the maximum possible product < 8. Subtract 6
from 8 and bring down 4.
Step 4: 24 is the new partial dividend. Here, 6 × 4 = 24.
Subtract 24 from 24. Now, nothing is left and no
number is left to bring down. So, stop.
Thus, Quotient = 84,014 and Remainder = 0.

Checking:
Quotient × Divisor + Remainder = Dividend

84,014 × 6 + 0 = 5,04,084 + 0 = 5,04,084. The division is correct.

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