P4 Factors and Multiples: Line Up the Tiles

Twelve violet square tiles tumble onto a mint table, one after another, and land in a loose heap. "Anya has 12 square tiles. How many rectangles can she make with all 12?"

That is Factor Finder, a 30-second Primary 4 episode of our Topic Explainers series. Factors can feel like a list of numbers to memorise, but this video makes them something your child can see: line the tiles up into a rectangle, and its sides are factors. Watch it first, then read on for the method behind each step.

Factor Finder: line them up, find the factors.

The video moves through four ideas: the factor pairs of 12, whether 5 and 7 are factors of 42, the common factors of 12 and 18, and the common multiples of 4 and 6. All four come from Factors and Multiples in Primary 4 Whole Numbers in the Singapore syllabus.

The method

A factor makes a rectangle with nothing left over

A factor of a number divides it exactly, with no remainder. With tiles, that means: if you can line up all the tiles in equal rows of that size, with none left over, the row size is a factor.

Twelve tiles can make a rectangle 3 rows of 4. So 3 is a factor of 12, and so is 4. Together, 3 and 4 are a factor pair of 12, because 3 × 4 = 12.

Factors and multiples are two sides of one fact

The same multiplication fact can be read two ways. From 3 × 4 = 12:

3 and 4 are factors of 12.
12 is a multiple of 3, and a multiple of 4.

A quick way to keep the words apart: the factors of 12 are never bigger than 12, while the multiples of 4 start at 4 and keep growing.

Find every factor, in order

To find all the factors of a number, try 1, then 2, then 3, and so on, writing each factor pair as you find it. Stop when the pairs start to repeat. For 12, after 3 × 4 the next pair would be 4 × 3, which is the same rectangle turned round. The list is complete.

Is it a factor? Divide and look at the remainder

To check whether a 1-digit number is a factor, divide by it. No remainder means yes. Any remainder means no.

Common factors and common multiples

A common factor of two numbers is on both of their factor lists. A common multiple is on both of their multiple lists. In both cases: list each number's set, then circle the numbers that appear in both.

Worked examples

All the numbers below are the ones in the video.

Example 1: how many rectangles can 12 tiles make?

Anya has 12 square tiles. Using all 12 each time, what rectangles can she make? What are the factors of 12?

Step 1: Try rows of 1. One long row of 12: 1 × 12.

Step 2: Try rows of 2. 2 rows of 6: 2 × 6.

Step 3: Try rows of 3. 3 rows of 4: 3 × 4.

Step 4: Try 4 and stop. 4 would give 4 × 3, the same rectangle as 3 rows of 4, turned round. So there are 3 rectangles.

Step 5: Collect the side lengths. Each side of each rectangle is a factor. In order, the factors of 12 are 1, 2, 3, 4, 6 and 12.

Why is 5 not on the list? Try it: 12 tiles in rows of 5 gives 2 rows and 2 tiles left over. No rectangle, so 5 is not a factor of 12.

Example 2: is it a factor of 42?

Is 5 a factor of 42? Is 7 a factor of 42?

Test 5. Line 42 tiles up in rows of 5. You get 8 full rows (8 × 5 = 40) and 2 tiles left over. There is a remainder, so 5 is not a factor of 42.

Test 7. Line them up in rows of 7 instead. You get 6 full rows (6 × 7 = 42) and none left over. 7 is a factor of 42.

Read it the other way. Because 6 × 7 = 42, 42 is a multiple of 7. One fact, two words.

A quick check for 5 that your child may know: multiples of 5 end in 0 or 5. 42 ends in 2, so 5 cannot be a factor.

Example 3: common factors of 12 and 18

Find the common factors of 12 and 18.

Step 1: List the factors of 12. From Example 1: 1, 2, 3, 4, 6, 12.

Step 2: List the factors of 18. Use factor pairs: 1 × 18, 2 × 9, 3 × 6. The next try, 4, leaves a remainder and 5 does too, and 6 is already in a pair, so the list is complete: 1, 2, 3, 6, 9, 18.

Step 3: Line up the lists and circle the matches.

Factors of 12	1	2	3	4	6	12
Factors of 18	1	2	3	6	9	18

The common factors of 12 and 18 are 1, 2, 3 and 6.

The last scene, in brief: common multiples of 4 and 6

The video's last number scene is a wall of number tiles from 1 to 40. The multiples of 4 get one mark (4, 8, 12, 16, 20, 24, 28, 32, 36, 40) and the multiples of 6 another (6, 12, 18, 24, 30, 36). The tiles with both marks are the common multiples of 4 and 6 up to 40: 12, 24 and 36. Our post on common multiples in P4 works through this method step by step.

Try one at home

Find the factors of 20. Is 3 a factor of 20? What are the common factors of 12 and 20?

The factor pairs of 20 are 1 × 20, 2 × 10 and 4 × 5, so the factors are 1, 2, 4, 5, 10 and 20. 3 is not a factor: 6 rows of 3 is 18, with 2 left over. Comparing with the factors of 12 (1, 2, 3, 4, 6, 12), the common factors of 12 and 20 are 1, 2 and 4.

Common mistakes

Leaving out 1 and the number itself. Every whole number has 1 and itself as factors: one long row of tiles always works. Start every list with that pair.
Missing a pair in the middle. Children often find 1 × 12 and 2 × 6 and stop. Trying 1, 2, 3, 4 in order, without skipping, finds every pair.
Counting the same rectangle twice. 3 rows of 4 and 4 rows of 3 are the same rectangle turned round, so 12 tiles make 3 rectangles, not 6.
Mixing up factors and multiples. If a child lists 24 as a factor of 12, ask, "Can 12 tiles make a row of 24?" Factors of a number are never bigger than the number.
Calling a near miss a factor. 42 in rows of 5 is "almost" 8 rows, but 2 tiles are left over. Any remainder at all means it is not a factor.
Listing the common factors as all the factors. For 12 and 18, the answer is only the numbers on both lists: 1, 2, 3 and 6, not 4, 9, 12 or 18.

Parent tips

Use real tiles. Square crackers, coins, buttons or building blocks all work. Give your child 12, 18 or 24 and ask for every rectangle they can make. Write each one as a multiplication fact.
Turn it into a remainder test. Give a handful of 30 to 50 items and ask, "Can we share these into rows of 6 with none left over?" Then check by lining them up.
Say both sentences. For every fact like 6 × 7 = 42, ask for both readings: "6 and 7 are factors of 42" and "42 is a multiple of 6 and of 7".
Make it a pattern hunt. Some numbers make only one rectangle, a single long row. Others, like 12 or 24, make several. Ask your child to find a few of each and notice which numbers allow more rectangles.
Keep the times tables warm. Finding factors quickly rests on knowing the times tables well. A few minutes of times-table practice makes the factor work much lighter.

More practice on just this skill

Near the end of the video, a skill card slides up with a "Whole Numbers" chip and one highlighted row, "Factors and Multiples", with a "Practise this skill" pill beside it. "Want more practice on just this? Pick one skill and practise only that."

That is targeted subtopic drills in Singapore Math Drills: practise exactly one skill instead of a whole unit, straight from the skill map. If factors are the shaky part of Whole Numbers, your child can practise factors and multiples on their own, without working through every other topic in the unit first.

And practice stays calm by design: no guilt-tripping over a missed day and no dark patterns, with your child's progress only ever measured against their own. Line them up, find the factors.

Try a sample

Try a free interactive Primary 4 worksheet and see how calm practice feels, with no signup or credit card required.

Try a free Singapore math sample