Long Division
Divide, multiply, subtract and bring down repeatedly to get the quotient.
Key idea
Divide, multiply, subtract and bring down repeatedly to get the quotient.
In depth
Long division repeats four steps: divide, multiply, subtract, bring down. Each step finds one digit of the quotient by asking how many times the divisor fits into the current part of the dividend.
Worked example
742 ÷ 3: 3 into 7 = 2, 7−6=1; bring down 4 → 14; 3 into 14 = 4, 14−12=2; bring down 2 → 22; 3 into 22 = 7, 22−21=1. Answer 247 remainder 1.
Real-world uses
- Sharing a large prize among many winners
- Converting totals into per-person amounts without a calculator
Common mistake
Skipping a zero in the quotient when the divisor does not fit into a partial dividend.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Long Division?
Divide, multiply, subtract and bring down repeatedly to get the quotient. It is a topic at the intermediate level in Arithmetic & Number Sense.
Where is Long Division used in real life?
Real-world examples: Sharing a large prize among many winners; Converting totals into per-person amounts without a calculator.
What should I learn before Long Division?
Make sure you are comfortable with Long Multiplication, the previous topic in Arithmetic & Number Sense.
What is a common mistake with Long Division?
Skipping a zero in the quotient when the divisor does not fit into a partial dividend.
How can I practise Long Division?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Long Division?
Move on to Factors and Multiples next.
Related intermediate topics in Arithmetic & Number Sense
- Long Multiplication – Multiply by each digit of the multiplier, shift by place value, then add partial products.
- Factors and Multiples – Factors divide a number exactly; multiples are its products with whole numbers.
- Divisibility Rules – Quick tests: by 2 last digit even, by 3 digit-sum divisible by 3, by 5 ends 0/5, by 9 digit-sum divisible by 9.
- Prime Numbers – A prime has exactly two positive divisors: 1 and itself.
- Composite Numbers – Numbers greater than 1 with more than two factors.
- Prime Factorization – Every integer above 1 is a unique product of primes.