Prime Time: common misconceptions

If your child says… “One and the total itself don't count as factors.”

Ask together

How many rows are there, and how many beans are in each row?

What’s true

Single rows show that 1 and the total both count.

If your child says… “Any number that shares both is the greatest common factor.”

Ask together

Can we make more than three identical portions without leftovers?

What’s true

The greatest common factor is the largest count that works.

If your child says… “I cross out 2 along with its multiples.”

Ask together

Which factor does 2 have besides 1 and itself?

What’s true

The sieve keeps each prime and removes its larger multiples.

If your child says… “Both numbers must be prime to be co-prime.”

Ask together

Which factor greater than 1 do 8 and 9 share?

What’s true

Composite numbers can still be co-prime.

If your child says… “I always multiply the numbers to find their first common multiple.”

Ask together

Did we clap together before reaching 24?

What’s true

Their product is a common multiple, but an earlier one may work.

If your child says… “Two times six is already a prime factorisation.”

Ask together

Can six still split into factors greater than 1?

What’s true

Every factor must be prime before the splitting is finished.

If your child says… “For 4, I only check the last digit.”

Ask together

Can 34 split into fours without a remainder, even though it ends in 4?

What’s true

Divisibility by 4 depends on the number formed by the last two digits.

If your child says… “If the rows work, the grid is finished.”

Ask together

Does your entry also make its column product match?

What’s true

Every row and every column must give its stated product.