Grade 3 Factors and Multiples Worksheets — Free Printable PDF
This is the gentle start of a topic that matters later. Two sheets sit on this page, and both ask about one number at a time rather than setting a sum to be worked out. Factors runs Factor pairs, which writes 24 as 1 × 24, 2 × 12 and 3 × 8; then Every factor listed, which unpacks the same information into one ascending line; then Is it a factor?, which asks a yes-or-no question and wants the partner factor written down as proof rather than a bare Yes. Multiples runs The first few, counting up in a number from 2 to 9; then Spot the multiple, where exactly one of four printed numbers really is a multiple of the target and the other three are near misses a digit or two either side; then Multiples in a range, which makes a child find the first multiple past the floor instead of counting from the beginning.
Every number the Factors sheet asks about is between 12 and 70 and has at least three factor pairs in it, so there is always something to find and never so much that the exercise turns into copying. That is the whole difference between this page and the Grade 4 one, which keeps these twenty-two numbers and carries on to 100. Every list answer runs smallest first and the instruction line above the questions says so, so a parent marking from the key never has to decide whether a different order should count. Set the level and the number of questions — anything from four to twenty — and tick the answer key box for a separate solutions page. Shuffle builds a fresh set at the same settings, the sheets print clean in A4 or US Letter, and the link in your address bar rebuilds this exact worksheet whenever you open it.
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Factors & Multiples · Grade 3
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Grade 3 · 3 pages · A4More Grade 3 factors & multiples skills
Each one generates a different kind of question, with its own three levels and answer key.
What each level generates
Grade 3 factors — the exact skill behind each difficulty setting, straight from the generator.
- Level 1Factor pairs
- Level 2Every factor listed
- Level 3Is it a factor?
Grade levels follow the progression common to most English-language curricula — not one specific national curriculum. Every level shows exactly what it generates, so you can check the fit with your own program. See the full scope & sequence →
Where this page sits in the curriculum — and where it does not
Be clear about this one, because it affects how you use the page. Factor pairs are named by the Common Core at Grade 4, in 4.OA.B.4, and by the English curriculum in Year 4. There is no Grade 3 standard for them in either framework, and this page does not pretend otherwise: it is an on-ramp rather than a requirement, and the page that claims 4.OA.B.4 is the Grade 4 one.
What Grade 3 does have is the ground this stands on. CCSS 3.OA.C.7 asks for fluent multiplication and division within 100, and 3.OA.D.9 asks a student to identify arithmetic patterns — which is exactly what the Multiples sheet is. The English Year 3 programme asks for counting in multiples of 4, 8, 50 and 100. So the Multiples half of this page is squarely on-standard, and the Factors half is a head start for a child whose tables are already secure.
That suggests an order of use. If the tables are still being learned, spend the time on Times Tables and Multiplication instead and come back to this. If they are solid and the child is ready for something that is not another page of products, the Factors sheet gives the same facts a new job — and a year later, when the vocabulary arrives formally, it will already be familiar rather than new.
Working in pairs, from the outside in
Almost every wrong answer on the Factors sheet is a list that stopped early rather than a list with something wrong in it, and the same two factors go missing more often than all the rest together: 1 and the number itself, which feel too obvious to write down, and the pair in the middle, which is the one that actually has to be searched for.
Working outside in fixes both. For 40 that is 1 and 40, then 2 and 20, then 4 and 10, then 5 and 8 — and you stop when the two sides of the pair meet. That is precisely what Factor pairs drills before Every factor listed asks for the same information as a single ascending line. Because the key is in order and the sheet says so, a missing factor shows up as a gap in the middle of a line rather than a wrong number at the end, so marking takes seconds. When a list comes back short, do not read the key out — ask for it back in pairs and let the gap find itself.
On the Multiples sheet the slip is different in kind. A child who has learned the first five multiples of a number as a chant can produce them without dividing anything, which is why Spot the multiple prints near misses rather than random numbers: 21 among 19, 21, 52 and 66 has to be picked by knowing the 7s, not by the shape of the number.
What eight questions a couple of times a week buys
Keep the sheets short. The thinking here is per question rather than per page — a child listing the factors of 36 is doing four or five separate divisions and a decision about when to stop — so eight to ten questions two or three times a week is plenty, and twenty is a stretch session rather than a normal one.
The payoff is further out than most sheets on this site, and it is worth knowing what it is. The fractions pages ask children to cancel an answer to lowest terms and, later, to add two fractions whose denominators differ. Both quietly assume something nobody teaches directly: that a child can look at 18 and 24 and see what they share. Times tables give the facts and multiplication gives the operation, while fractions spend the knowledge. This topic is the step in between, and starting it here means the Grade 4 page is a widening rather than an introduction.
A child who finishes this page should be able to say what a factor is, what a multiple is, which way round the two words go for a given pair of numbers, and produce a complete factor list for a number under 70 without being prompted for the ends.
Frequently asked questions
▸Is Grade 3 too early for factors?
For the vocabulary, slightly — factor pairs are a Grade 4 standard in the Common Core (4.OA.B.4) and a Year 4 objective in England, and this page says so rather than claiming otherwise. The Multiples sheet is a different matter: counting in equal steps and spotting patterns is Grade 3 work in both frameworks. Use this page when the tables are secure and you want those facts doing something new; if they are not secure yet, the times tables sheets are the better use of the time.
▸What is the difference between a factor and a multiple?
A factor divides into the number; a multiple is what you land on counting up in it. 6 is a factor of 24, and 24 is a multiple of 6 — one pair of numbers read in two directions. This page has a sheet for each direction, which is the quickest way to stop the two words swapping places.
▸How is this different from the Grade 4 factors page?
Size, not kind. Both pages carry the same two sheets with the same three levels. Grade 3 asks about twenty-two numbers between 12 and 70 and counts in numbers from 2 to 9; Grade 4 keeps every one of those and carries on to 100, counting in numbers up to 12. Nothing on this page is missing from Grade 4 — it is the first half of the same ladder, so a child can move up without meeting a new kind of question.
▸Do the answers have to be in a particular order?
Yes, and the sheet says so in the line above the questions. Every list answer is smallest first, and factor pairs are ordered by their smaller number, starting at 1. That is deliberate on both counts: a key accepting any order would be slow to mark, and a key demanding an order the sheet never mentioned would be unfair.
▸Are prime numbers or the highest common factor on these sheets?
No. This page has two sheets only — Factors and Multiples. Primes and composites, divisibility rules and prime factorisation start on the Grade 5 page, and the highest common factor and lowest common multiple are on the Grade 6 one. Deciding a number is prime means showing that nothing divides it, and the tool for that is a complete factor list, which is the skill this page is still building.
▸How is this different from a times tables worksheet?
A times tables sheet asks for a product, and both it and the multiplication sheets already carry a missing-number drill of the 4 × ___ = 24 kind. Nothing here repeats that. Every question on this page is a sentence about one number — list its factors, write its pairs, say whether something divides it — and the × sign appears only in an answer, where a factor pair is the natural way to write one.