Prime Numbers Worksheets Generator

Three modes

Identify asks whether a given number is prime. Factorise asks for the prime factorisation. Range list asks for every prime between two numbers.

Twenty questions by default with a ceiling of 100, both adjustable.

Which mode when

Identify comes first and is the quickest to mark. It builds the divisibility habits that everything else rests on — even numbers go, digit sums divisible by 3 go, anything ending in 0 or 5 goes, and after those three tests remarkably few candidates are left.

Factorise is the one that matters most later. Prime factorisation is how you find a highest common factor, a lowest common multiple, and how you simplify a surd or a fraction with any confidence.

Range list is the slowest and the best for a lesson starter done as a class. It rewards system over speed, and a pupil who works it by sieving beats one who tests each number in turn.

The definition trips people

A prime has exactly two distinct factors: 1 and itself.

Which means 1 is not prime — it has only one factor — and this is not a technicality invented to annoy pupils. If 1 were prime, every number would have infinitely many factorisations, and the whole point of prime factorisation is that each number has exactly one. Two is prime, and it is the only even prime, which children find suspicious and worth discussing.

Factor trees

The standard method, and the useful property is that it does not matter where you start. Break 60 as 6×10 or as 4×15 or as 2×30, and you arrive at 2² × 3 × 5 every time.

Demonstrating that once, with two different starting splits side by side on the board, does more for understanding the fundamental theorem of arithmetic than stating it does.

Setting the ceiling

A hundred is right for first work: there are 25 primes below it, and the largest number a pupil needs to test against is 7, since anything composite under 100 has a factor of 7 or less.

Raise it to 200 or 500 for stretch, and mention the general rule — you only need to test divisors up to the square root. It converts an intimidating job into a short one, and it is the sort of insight that makes a pupil feel mathematics is on their side.

Related

Factors and multiples is the natural companion sheet.