Factors, Multiples & Primes Worksheets

For each number under 100, circle every one-digit number from 2 to 9 that divides it evenly.

Find all the factors and factor pairs of a number, and decide whether a number is a multiple of a one-digit number.

Explore prime and composite numbers two ways: circle the primes in each group, or work through the hands-on Rectangle Test discovery lab.

The digits of every multiple of 9 add up to 9 — and the rule runs both ways. A lab that builds the pattern from the 9s facts, tests the converse, pushes it past 100, and uses it to spot errors and find missing digits.

Write each number as a product of prime numbers by filling in the boxes.

Discover the quick tests for multiples — 2, 5, 10, 4 and 8 — by working out why they work, with real applications like leap years, the Olympics, quarters and coins.

Deductive number puzzles: use a set of clues to pin down one hidden mystery number, or find a pair of mystery numbers from clues about their GCF, LCM, or sum.

Practice prime numbers: list the primes in a range, test whether a larger number is prime, find prime pairs, and write prime factorisations — discovering along the way why you only need to check divisors up to a number's square root.

Work backwards from a number’s proper factors (every factor except itself): name the mystery number from its proper factors, fill the gaps in a factor list, and sort numbers as perfect, abundant, or deficient. Pairs with The Factor Game.

Reason about factors, multiples, primes, GCF and LCM: decide whether statements are always, sometimes, or never true, and build sets of numbers that satisfy a given condition — justifying with examples.

Break a number into a factor string with a product puzzle or a factor tree, then find the longest string of all — its prime factorization — in expanded and exponent form.

Find the greatest common factor (GCF) of a pair of numbers.

Find the least common multiple (LCM) of a pair of numbers.

The classic 1000-lockers puzzle: the lockers left open turn out to be exactly the perfect squares — because only a perfect square has an odd number of factors. Explore the lab, then count any number’s factors from its prime factorization.

Spot when a situation needs the greatest common factor and solve it.

Spot when a situation needs the least common multiple and solve it.

Word problems built on the Factor Game (from CMP "Prime Time"). Each problem sets up a game on a 1–N board (1–30 up to 1–100) and asks three things: score the factors a first move gives away, find the best first move, and reason about abundant and perfect numbers. Every part is scored exactly in the answer key.