Long Division

Long division is a step-by-step method for dividing large numbers. It helps you break down a big division problem into smaller, easier steps.

In this lesson, we’ll walk you through two examples:

• 3-digit number divided by a 2-digit number → 364 ÷ 30
• 4-digit number divided by a 1-digit number → 1615 ÷ 7

Let’s use long division to divide 364 by 30.

1. Set it up:
   • 364 is the dividend (the number being divided).
   • 30 is the divisor (the number you’re dividing by).
2. Divide the first digits:
   • 30 goes into 36 once.
   • Write 1 above the 6 in the quotient area.
   • Multiply: 1 × 30 = 30
   • Subtract: 36 − 30 = 6

3. Bring down the next digit (4):

   • Now you have 64

4. Divide again:

   • 30 goes into 64 two times.
   • Write 2 in the quotient
   • Multiply: 2 × 30 = 60
   • Subtract: 64 − 60 = 4
5. Result:
   • As there are no more digits to bring down, so 12 is the quotient, and 4 is the remainder.
   • So: 364 ÷ 30 = 12 R 4

To check your long-division answer, use this formula:

$$ \text{Quotient} \times \text{Divisor} + \text{Remainder} = \text{Dividend} $$

For example, you solved:

$$ 364 \div 30 = 12\ \text{R}\ 4$$

Let’s identify each part:

• Dividend = 364 → the number being divided
• Divisor = 30 → the number you’re dividing by
• Quotient = 12 → how many whole times 30 fits into 364
• Remainder = 4 → what’s left over

Substitute the numbers:

$$ 12 \times 30 + 4 = 360 + 4 = 364$$

It matches the original number (364), so the division is correct! ✅

Let’s use long division to divide 1615 by 7.

• Set it up:
  • 1615 is the dividend (the number being divided).
  • 7 is the divisor (the number you’re dividing by).
• Divide the first digits:
  • 7 goes into 16 two times.
  • Write 2 above the 6 in the quotient area.
  • Multiply: 2 × 7 = 14
  • Subtract: 16 − 14 = 2
• Bring down the next digit (1):
  • Now you have 21
  • 7 goes into 21 three times.
  • Write 3 in the quotient
  • Multiply: 3 × 7 = 21
  • Subtract: 21 − 21 = 0
• Bring down the last digit (5):
  • Now you have 5
  • 7 goes into 5 zero times.
  • Write 0 in the quotient
  • Subtract: 5 − 0 = 5

• Result:

  • There are no more digits to bring down, so the quotient is 230, and the remainder is 5.
  • So:  1615 ÷ 7 = 230 R 5

To double-check that your calculation is correct, use this formula:

$$ \text{Quotient} \times \text{Divisor} + \text{Remainder} = \text{Dividend} $$

$$ 230 \times 7 + 5 = 1610 + 5 = 1615$$

It matches the original number (1615), so the division is correct! ✅