Free printable factors and multiples chart
Grades 4–6What divides into a number and what a number divides into, plus how to find the greatest common factor and the least common multiple. Print it for the wall, or put any two numbers into the tool below and see both lists side by side.
Tap the chart to open it at full size
Compare any two numbers
Enter two numbers and you get all the factors of each and the first ten multiples of each. Anything appearing in both lists turns purple, and the answer turns green — the biggest of the shared factors, the smallest of the shared multiples.
Start with 12 and 18. Their factors share 1, 2, 3 and 6, so the GCF is 6. Their multiples share 36 and 72 within the first ten, so the LCM is 36. Both answers are visible rather than calculated, which is the point.
Then try 6 and 7. Nothing is shared except 1, which makes them coprime, and their LCM is the full 42. Comparing that against 12 and 18 — where the LCM is 36 rather than 216 — shows what the shared factor is actually doing.
- Greatest common factor
- GCF of 12 and 18 = 6
- Least common multiple
- LCM of 12 and 18 = 36
Purple squares appear in both lists. The green one is the answer — biggest of the shared factors, smallest of the shared multiples.
How to use this factors and multiples chart at home
Pin the two words down before anything else. Factors are inside a number — they divide in, and they stop at the number itself. Multiples run away from it — they are what you count in, and they go on forever. Children who have that straight rarely get anything else wrong here.
Find factors in pairs, out loud. For 24, say one twenty-four, two twelve, three eight, four six. The rhythm of pairing is what stops factors going missing, and missing factors are the commonest error in the whole topic.
Use the tool above when a fraction will not simplify. Put the numerator and denominator in, read off the GCF, divide once, and you are done. It is much faster than halving repeatedly and hoping, and it shows why the GCF is worth finding at all.
Why these two ideas earn their place
On their own, factors and multiples look like vocabulary. Their value is entirely in what they unlock two topics later, and it is worth saying that out loud to a child who asks why they are listing the factors of 36.
The GCF is how you simplify a fraction in one move instead of three. 18/24 has a GCF of 6, so it goes straight to 3/4. A child without that tool halves it to 9/12, then divides by 3, and often stops somewhere in the middle.
The LCM is how you add fractions. To do 1/4 + 1/6 you need a common denominator, and 12 — the LCM — keeps the numbers small. Multiplying the denominators gives 24, which also works but leaves you simplifying afterwards.
Finding factors without missing any
Start at 1 and work up, writing both numbers of each pair. For 36: 1 and 36, 2 and 18, 3 and 12, 4 and 9, 6 and 6. Then stop, because 6 × 6 has reached the square root and everything beyond it has already been written down as the partner of something smaller.
That stopping point is the same idea as the prime-testing rule: factors come in pairs straddling the square root, so once you reach it you have them all. It turns an open-ended hunt into a short, finite list.
Square numbers are the exception worth noticing. 36 has 6 × 6, where both halves of the pair are the same number, which is why square numbers always have an odd number of factors. Children find that genuinely surprising.
Where factors and multiples usually go wrong
Swapping the two words. Listing the multiples when the question said factors. The words sound related and point in opposite directions, and the fix is repetition rather than explanation.
Missing the large factor of a pair. Finding 3 divides into 36 and not writing 12 alongside it. Always write both halves at once.
Forgetting 1 and the number itself. Every number has both, and they are the ones most often left off a list.
Assuming the LCM is the product. It is a common multiple, but only the least one when the two numbers share nothing. When they do share a factor, multiplying overshoots and makes the fraction work harder than it needs to be.
After the chart goes up
A chart explains the idea but gives a child nothing to do. These do the rest.
- factors multiples at Mathify Kids — every topic in this area, sorted by grade.
- factors and multiples worksheets — printable practice.
- greatest common factor worksheets — the next step once this is solid.
- least common multiple worksheets — more practice in the same area.
Everything at this level: Grade 4 math · Grade 5 math · Grade 6 math
Charts that pair with this one
Charts that work well printed alongside this one.
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Prime and Composite Numbers chart
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Multiplication chart
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Division chart
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Fractions chart
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Estimation and Rounding chart
Last reviewed
Questions parents ask
What is the difference between a factor and a multiple?
A factor divides into a number exactly and is never bigger than it. A multiple is what you get by multiplying that number and is never smaller. 3 is a factor of 12; 12 is a multiple of 3. The same pair of numbers, described from opposite ends — which is exactly why the words get muddled.
How do you find all the factors of a number?
Work in pairs from 1 upwards. For 24: 1 × 24, 2 × 12, 3 × 8, 4 × 6. Then check 5, which does not go, and stop at 5 because 5 × 5 is already past 24. Pairing guarantees you catch the large factors alongside the small ones, which is where factors normally get missed.
What is the greatest common factor?
The largest number that divides into both. For 12 and 18 the shared factors are 1, 2, 3 and 6, so the GCF is 6. It is what you use to simplify a fraction in one step: 12/18 divided top and bottom by 6 gives 2/3 immediately.
What is the least common multiple?
The smallest number that both divide into. For 4 and 6 it is 12. It is what you need when adding fractions with different denominators, because it gives the smallest common denominator that works and keeps the numbers manageable.
Is the LCM always the two numbers multiplied together?
Only when they share no factors. 6 and 7 have an LCM of 42, which is 6 × 7. But 12 and 18 have an LCM of 36, not 216, because the factor 6 they share only needs counting once. Multiplying always gives a common multiple — just not usually the least one.
What grade is this factors and multiples chart for?
Grades 4 to 6. Factors and multiples usually arrive in Grade 4, GCF and LCM in Grade 5 or 6, and they get used constantly from then on for simplifying fractions and finding common denominators.
Is this factors and multiples chart free to print?
Yes. Open it full size and print as many copies as you need for home or a classroom, with no account and no watermark. Reselling it or re-hosting the file elsewhere is not allowed — link to this page instead.