Grade 6 Factors Worksheets — HCF, LCM and Prime Factors PDF
Grade 6 is the year the question changes from what one number is made of to what two numbers have in common, and that is the fact every fractions page has been waiting for. Five sheets sit on this page. It opens on Primes & Composites — Prime or composite?, then Find the primes from a printed list, then Show it is not prime, which asks for a factor pair as the proof and so cannot be guessed at. Divisibility Tests and Prime Factors are here too, and Divisibility Tests moves up to four-digit numbers at this grade, where no digit rule can be short-circuited by recognising the number.
The two new sheets are what the year is about. Common Factors & HCF runs Shared factors, which asks for every factor the two numbers have in common, then Highest common factor, then HCF of three. Common Multiples & LCM runs Shared multiples, then Lowest common multiple, then LCM of three. Every list answer is in ascending order and the instruction line above the questions says so. Set the level and the question count, tick the answer key box to put the solutions on their own page, and print in A4 or US Letter. There is room under each question to work in, Shuffle makes a fresh set at the same settings, and the link in your address bar rebuilds this exact sheet later.
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Factors & Multiples · Grade 6
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Grade 6 · 3 pages · A4More Grade 6 factors & multiples skills
Each one generates a different kind of question, with its own three levels and answer key.
- 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.
- Common Factors & HCFFind what two or three numbers share, and the largest factor common to them all.
- Common Multiples & LCMFind the numbers two or three counts land on together, and the first one of them.
What each level generates
Grade 6 primes & composites — the exact skill behind each difficulty setting, straight from the generator.
- Level 1Prime or composite?
- Level 2Find the primes
- Level 3Show it is not prime
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 6 factors should cover
CCSS 6.NS.B.4 is the standard here, and it asks for two things this page is built around: the greatest common factor of two whole numbers up to 100, and the least common multiple of two small ones. Common Factors & HCF covers the first, drawing its numbers from 12 to 96, inside the standard's range. Common Multiples & LCM covers the second, with pairs from 3 to 12 on Shared multiples and from 4 to 15 on Lowest common multiple, so the second of those reaches a little past the ceiling of twelve the standard names. HCF of three and LCM of three go further still, and they are where guessing stops working. The one part of 6.NS.B.4 not on this page is its distributive-property clause, rewriting 36 + 8 as 4 × (9 + 2), which is expression work rather than factor work.
Two of the other sheets here also appear on the Grade 5 page, and both move up a band rather than repeating one. Primes & Composites changes range outright: Grade 5 decides numbers from 11 to 99, where a table a student already knows usually settles it, while this grade works from 101 to 199, where 143 and 187 have to be tried against 7, 11 and 13 before anything can be said about them. Prime Factors runs higher at every level too, reaching 200, 900 and 800 across its three where Grade 5 reaches 100, 400 and 300. Divisibility Tests changes most visibly of the three — three-digit numbers at Grade 5, four-digit numbers here — since a four-digit number puts the digit rules beyond any chance of being recognised outright.
The two facts every fractions page is waiting for
The fractions worksheets on this site ask children to give an answer in lowest terms, and to add or subtract fractions whose denominators differ. Both instructions assume a fact about two numbers that nothing on the site used to teach. The highest common factor is what cancels a fraction to lowest terms in one step, and the lowest common multiple is the common denominator. A child who reduces 18/24 to 9/12 and then to 3/4 has taken two goes at it because they found a common factor rather than the highest one, and a child who adds sixths and eighths over 48 has used a common multiple rather than the lowest, which is 24.
So the shortest route to better fractions marks is often not another fractions sheet. If simplifying keeps coming back half-done, spend a week on Highest common factor and then mark the same fractions answers again. If unlike denominators are the problem, Lowest common multiple is the sheet, and Shared multiples is the gentler way into it: its numbers are smaller, and it asks for the first two numbers both counts land on rather than naming the smallest one outright.
Why the shortcuts work, and where three numbers break them
Both shortcuts fall out of prime factorisation, which is why that sheet is still on this page. Write each number as primes — 24 is 2 × 2 × 2 × 3 and 36 is 2 × 2 × 3 × 3 — and the highest common factor is what the two lists hold in common, 2 × 2 × 3, which is 12, while the lowest common multiple is what covers both lists, 2 × 2 × 2 × 3 × 3, which is 72. Neither is a trick to be memorised. Both are consequences of a number having exactly one prime factorisation, so once the primes are on the page there is nothing left to decide.
LCM of three is where a habit that has been working quietly stops working. Multiplying two numbers together and dividing by their highest common factor gives the lowest common multiple, and plenty of students shorten that to just multiplying, which survives on a pair sharing nothing and fails everywhere else. With three numbers it fails loudly: the lowest common multiple of 3, 4 and 6 is 12, not 72. The reliable method is to take them two at a time — find the answer for the first two, then bring the third number in against that answer — and it works the same way for the highest common factor.
Frequently asked questions
▸What is the difference between the HCF and the LCM?
The highest common factor is the largest number that divides into both, so it is never bigger than the smaller of the two. The lowest common multiple is the smallest number both divide into, so it is never smaller than the larger of the two. Saying those two boundaries out loud catches most wrong answers before they are written down.
▸Is the HCF the same as the GCF?
Yes. Highest common factor is the British name and greatest common factor the American one, and greatest common divisor or GCD means the same again. CCSS 6.NS.B.4 calls it the greatest common factor; the questions on these sheets say highest common factor throughout, so tell your student the two names are one idea before they meet the other one in a textbook.
▸How do you find the HCF or LCM of three numbers?
Two at a time. Find the answer for the first two numbers, then find it again for that answer and the third number. It works for both, and HCF of three and LCM of three are built for exactly this — it is also the level where multiplying everything together stops giving the right answer, since the lowest common multiple of 3, 4 and 6 is 12 rather than 72.
▸How does this help with fractions?
Directly. The highest common factor is what takes a fraction to lowest terms in one move — 18/24 has an HCF of 6, so it goes straight to 3/4 rather than through 9/12 — and the lowest common multiple of two denominators is the common denominator you need before adding or subtracting them. Both skills are on this page.
▸Are the primes and prime factors sheets the same as the Grade 5 ones?
No — both move up at this grade. Prime or composite? and Find the primes work from 11 to 99 at Grade 5 and from 101 to 199 here, which is the point where a known table stops settling the question and a number like 143 or 187 has to be tried against 7, 11 and 13. Prime Factors runs higher at every level too, reaching 200, 900 and 800 where Grade 5 reaches 100, 400 and 300. Divisibility Tests changes as well, from three-digit numbers at Grade 5 to four-digit numbers here, and the two common-factor and common-multiple sheets are new at this grade.