Real Numbers: common misconceptions

If your child says… “Four times three is already a prime factorisation.”

Ask together

Can four still be split into smaller factors?

What’s true

Keep splitting until every factor is prime.

If your child says… “A much larger power might finally end in zero.”

Ask together

Where could a factor of five enter this multiplication?

What’s true

Repeating multiplication changes prime counts but introduces no new primes.

If your child says… “The HCF takes the larger powers because it means highest.”

Ask together

Could thirty-six divide twelve exactly?

What’s true

LCM takes every prime's greatest required count, while HCF takes each shared prime's smallest count.

If your child says… “Multiplying the numbers always gives their LCM.”

Ask together

Does multiplying six and ten count their shared two once or twice?

What’s true

Multiplying gives the LCM directly only when the highest common factor is one.

If your child says… “The next shared tap uses the HCF.”

Ask together

Would both taps be due at the highest common factor?

What’s true

A shared tap must complete whole intervals of both lengths.

If your child says… “A shared factor contradicts the denominator being nonzero.”

Ask together

Can an even denominator still be nonzero?

What’s true

Lowest terms excludes shared factors greater than one, yet both numbers share factor two.

If your child says… “Even multiplying by zero keeps it irrational.”

Ask together

Does multiplying by zero leave any of the starting number?

What’s true

A rational multiplier preserves irrationality only when it is nonzero.