How to generate a division with no remainder (exact division)

When to use this: Use this method when you want students to perform a division and ensure that the result is always an exact integer (no decimals or remainders).

What you'll achieve: You will generate two integers (dividend and divisor) such that the division always produces a whole number result.

See it in action: Watch how this logic is implemented inside LearningLemur:

Before you begin

Requirements

• Basic knowledge of how to create a LearningLemur question
• Familiarity with adding an algorithm to generate random variables

Steps

Select a divisor

div = random(2,12)

This defines the divisor and avoids trivial cases like division by 1.

Select a quotient

quot = random(2,10)

This defines the exact integer result students should obtain.

Compute the dividend

dividend = div * quot

Multiplying the divisor and quotient yields a dividend that guarantees exact division.

Define the solution

solution = quot

This value can be used directly for grading.

Verify it worked

• Preview the question multiple times
• Divide the generated dividend by the divisor manually
• Confirm that the result is always an integer
• Ensure no decimal answers appear

Full algorithm (copy-paste version)

Use the complete version below if you want to copy the logic directly into your question algorithm:

# Select a random divisor from 2 to 12
div = random(2,12)

# Choose a random integer quotient between 2 and 10
quot = random(2,10)

# Compute dividend ensuring exact division
dividend = div * quot

# Students perform the division
solution = quot

Options and variations

• If you want larger numbers, you can increase the intervals for div and quot, but verify readability for students
• If you want to include negative results, you can allow negative values in the quotient range
• If you want to control difficulty, you can use prime divisors for easier mental calculation, or larger composite divisors for more complexity

Common errors

Unexpected decimal results

Ensure the dividend is defined as div * quot and not randomly generated

Division by zero error

Confirm the divisor interval excludes 0 (already handled in this example)

Trivial exercises (division by 1)

Adjust the divisor interval to avoid overly simple cases

Related

• Understanding Advanced Logic in LearningLemur
• Common Patterns and Best Practices
• Glossary of Commands