Grade 5 Factors, Primes and Divisibility Worksheets — Free PDF
Fifth grade is the year a number gets taken apart. Grade 4 asked what a factor and a multiple are; this page asks which numbers are prime, what divides what, and what a number is actually built from. Five sheets sit here, each with its own three levels, and the level control moves inside whichever sheet you are on.
Factors is still the sheet the page opens on, but the numbers have grown: Factor pairs and Every factor listed now run up to 200, and Is it a factor? usually reaches outside the times-table grid, so a question like "Is 7 a factor of 91?" has to be worked out rather than remembered — and it wants the partner factor as proof. Multiples counts in numbers up to 25. The three new sheets are the year's real content. Primes & Composites runs Prime or composite?, then Find the primes out of a printed list, then Show it is not prime, which cannot be guessed at because naming a factor pair is the proof. Divisibility Tests puts three-digit numbers under the digit rules: 2, 5 and 10 first, then 3, 6 and 9, then Which tests pass, where all seven are on the line at once. Prime Factors goes Break into primes, then Bigger numbers past 100, then Name the number, which hands over a factorisation and asks which number it belongs to. Tick the answer key box for a separate solutions page, print in A4 or US Letter, and use the link in your address bar to rebuild the exact sheet whenever you want it again.
Build your worksheet
Factors & Multiples · Grade 5
The link is the save: it reopens this exact worksheet — same questions, same settings. Bookmark it or send it on. No account needed.
Printed on the worksheet only — never saved or sent anywhere
Live preview
Grade 5 · 3 pages · A4More Grade 5 factors & multiples skills
Each one generates a different kind of question, with its own three levels and answer key.
- FactorsFind the factor pairs of a number, list every factor, and test whether one number divides another.
- MultiplesCount up in a number, spot its multiples among others, and find them inside a range.
- Primes & CompositesDecide whether a number is prime, pick the primes out of a list, and prove a number is not one.
- Divisibility TestsUse the digit rules to tell what divides a number without dividing it.
- Prime FactorsBreak a number down into the primes it is made of, and build it back up again.
What each level generates
Grade 5 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 →
What Grade 5 factors and primes should cover
England's Year 5 programme of study names this year directly: identify multiples and factors, including all the factor pairs of a number; know and use the vocabulary of prime numbers, prime factors and composite numbers; and establish whether a number up to 100 is prime, recalling the primes up to 19. Factor pairs, Every factor listed and the Multiples sheet cover the first of those. Primes & Composites covers the rest: Prime or composite? and Find the primes both work in the range 11 to 99, which is the range that objective describes, while Show it is not prime reaches past 100 to numbers like 143 and 187, whose single factor pair has to be found rather than remembered. The common-factor half of the same objective — what two numbers share — is on the Grade 6 page here, where it belongs with the highest common factor.
The Common Core puts factor pairs and the prime-or-composite decision a year earlier, in 4.OA.B.4, and never names prime factorisation as a standard of its own at any grade. That is not an argument for skipping it. It is the tool 6.NS.B.4 leans on at Grade 6, when the highest common factor and the lowest common multiple arrive, and a student meeting it for the first time in the same week as those two has two new things to hold at once. So this page teaches the tool a year before the standard that spends it, which is roughly where the English curriculum puts it anyway.
A divisibility test is a rule about digits, not a division
This is the sentence worth saying out loud, because a student who divides to answer a divisibility question has done the arithmetic and missed the point. 2, 5 and 10 are decided by the last digit alone. 3 and 9 are decided by whether the digits add up to a multiple of 3 or of 9. 4 is decided by the last two digits, and 6 asks only whether the 2 rule and the 3 rule both pass. Each level is named for the tests it uses: 2, 5 and 10 is the last-digit family, 3, 6 and 9 is the digit-sum family, and Which tests pass sets all seven going against one number — 2, 3, 4, 5, 6, 9 and 10. The numbers are three-digit ones at this grade precisely so that no answer can come from recall.
Work one aloud the first few times. Take 738: the last digit is 8, so 2 passes and 5 and 10 do not; 7 + 3 + 8 is 18, a multiple of 9, so 3 and 9 both pass; 6 needs 2 and 3, and it has them; 4 wants the last two digits, and 38 is not a multiple of 4. The answer is 2, 3, 6 and 9, in that order, because every list on this sheet is smallest first. None is a legal answer on every level here and the instruction line says so, so a child who genuinely finds nothing has not made a mistake.
What a prime factorisation is for
Every whole number above 1 has exactly one factorisation into primes. 180 is 2 × 2 × 3 × 3 × 5 and there is no second way to write it, and that uniqueness is not a curiosity — it is the reason the Grade 6 shortcuts work at all. Break into primes and Bigger numbers ask for the factorisation; Name the number runs the same fact backwards, printing 2 × 2 × 3 × 3 × 5 and asking which number it belongs to. That reversal is the level that proves the point, because a factorisation does not merely describe a number, it identifies one.
It is also where the fractions work on this site quietly starts paying off. The fractions pages ask children to cancel to lowest terms and to add fractions whose denominators differ, and both assume a child can see what two numbers share. Nothing on the site taught that until this topic existed. Prime factorisation is the honest answer to "how do I know I have cancelled far enough?" — once the primes are written out, the shared ones are visible on the page and there is nothing left to argue about.
Frequently asked questions
▸Is 1 a prime number?
No. A prime has exactly two different factors, 1 and itself, and 1 has only one factor altogether. The other question that always follows: 2 is prime, and it is the only even prime, because every other even number has 2 as a third factor. Prime or composite? never asks about either — every number on that level sits between 11 and 97.
▸What are the divisibility rules used on these sheets?
A number divides by 2 if it ends in an even digit, by 5 if it ends in 5 or 0, and by 10 if it ends in 0. It divides by 3 if its digits add to a multiple of 3 and by 9 if they add to a multiple of 9. It divides by 4 if its last two digits do, and by 6 if the 2 rule and the 3 rule both pass. All seven appear together on Which tests pass.
▸How do you write a number as a product of primes?
Divide by the smallest prime that goes in, then keep going with what is left until that is prime too. For 180: 180 ÷ 2 = 90, 90 ÷ 2 = 45, 45 ÷ 3 = 15, 15 ÷ 3 = 5, and 5 is prime. Write the primes you divided by, smallest first — 2 × 2 × 3 × 3 × 5 — which is the form the answer key uses.
▸Are there factor trees on these worksheets?
No. Every sheet in this topic is a list of worded questions, which prints identically on A4 and US Letter and leaves room to work under each one. A factor tree is a method rather than an answer, so draw one in that space if it helps — the sheet is asking for the finished product line.
▸How is this different from the Grade 4 factors page?
Grade 4 asks what a factor and a multiple are. Grade 5 asks which numbers are prime, what divides what, and what a number is built from, which is three sheets Grade 4 does not have. The two shared sheets grow as well: factor lists run to 200 instead of 100, multiples are counted in numbers up to 25 instead of 12, and Is it a factor? usually picks a number outside the times-table grid so it cannot be answered from memory.