Factors and multiples explained for parents (Australia)

Homework says "list the factors of 12" or "circle the multiples of 5" - and Australian parents wonder whether that is the same as times tables, division, or something new again. In primary classrooms, factors and multiples are two sides of the same multiplication–division picture. A factor of a number is a whole number that divides it exactly (no remainder). A multiple of a number is what you get when you skip-count by that number - the products of its times table. Factors "go into"; multiples "come out of."

This guide owns that factors ↔ multiples distinction for Year 2–Year 5 (Prep light): clear definitions, factor pairs, a light touch on common factors, and hands-on practice before worksheets. Sibling zoom pages stay deeper on one picture each - equal groups (groups of), arrays (rows × columns), times tables explained and times tables without tears (fluency), multiplication explained (umbrella × meaning), division (sharing and grouping), skip counting (hops), and odd and even. Year maps: Year 2–Year 5 maths.

Factors: numbers that divide exactly

A factor of a whole number is another whole number that divides it with no remainder.

• The factors of 12 are 1, 2, 3, 4, 6 and 12 - each of those divides 12 exactly.
• 5 is not a factor of 12, because 12 ÷ 5 leaves a remainder.
• Every whole number has at least the factors 1 and itself.

Teachers may say factor, divides evenly, goes into, or ask "What can I multiply to make 12?" Match class wording. Concrete test: with 12 counters, can they make equal groups with none left? Two sixes, three fours, four threes, six twos, twelve ones - those are the factor stories. Link to division and equal groups.

Multiples: skip-count products of a number

A multiple of a whole number is what you get when you multiply it by 1, 2, 3, 4… - the same list you hear when you skip-count by that number.

• Multiples of 5: 5, 10, 15, 20, 25…
• Multiples of 4: 4, 8, 12, 16, 20…
• 12 is a multiple of 3 (because 3 × 4 = 12) and a multiple of 4, 2, 6, and so on.

The multiples of 4 are the 4 times table products. This page owns the word multiple and its contrast with factor; fluency lives on times tables explained and times tables without tears. The multiplication umbrella still owns what × means.

Factors vs multiples: one contrast table

Parents (and children) often swap the two words. Keep one kitchen-table sentence:

Word	Plain meaning	Example with 12
Factor	A whole number that divides 12 exactly	1, 2, 3, 4, 6, 12
Multiple	A number you get by multiplying 12 (or skip-counting by 12)	12, 24, 36, 48…

Memory hook: factors fit in (go into the number); multiples stretch out (grow from it). After homework ask: "Does this ask what goes into 12, or what we land on when we skip-count by 12?"

Factor pairs

Factors usually arrive in pairs that multiply to the target number.

• For 12: 1 × 12, 2 × 6, 3 × 4 (and turnarounds 12 × 1, 6 × 2, 4 × 3).
• List calmly: start with 1 and the number itself, try 2, then 3, and stop when pairs repeat.

An array makes pairs visible: a 3-by-4 rectangle shows 3 and 4; rotate for 4 and 3. Equal groups show the same pairs as piles. Even numbers always have 2 as a factor; odd numbers do not - light link to odd and even.

Common factors (light touch)

When two numbers share a factor, that shared factor is a common factor.

• Factors of 12: 1, 2, 3, 4, 6, 12
• Factors of 18: 1, 2, 3, 6, 9, 18
• Common factors of 12 and 18: 1, 2, 3, 6

You do not need formal HCF language at home unless school uses it. "What numbers go into both?" with counters is enough for Year 3–Year 5. Keep this light - idea, not algorithms.

Concrete first: arrays, counters, skip-count chant

Abstract "list the factors of 24" lands better after hands-on stories:

Counter divide check. Share 12 counters into equal groups with none left. Each successful share names a factor (and its pair). Leftovers mean "not a factor" - division.

Array rectangles. Build 1×12, 2×6, 3×4 with tiles or Lego. Each rectangle is a factor pair; rotate for the turnaround (arrays).

Skip-count chant for multiples. Clap 5, 10, 15, 20… Ask "Is 20 a multiple of 5?" Yes - we landed on it (skip counting).

Equal-groups rebuild. Three groups of four → 12 → "3 and 4 are factors of 12; 12 is a multiple of 3 and of 4" (equal groups).

Keep sessions under ten minutes. Plates, pasta, Lego and scrap paper are enough. The win is naming which word applies, not a perfect grid.

Year by year: where factors and multiples show up

Prep / Year 1 - equal sharing and "groups of" more than the words factor/multiple (Prep maths; Year 1 maths).

Year 2 - equal groups, arrays and skip-counting become regular; factor/multiple language may appear lightly (Year 2 maths; AC Year 2).

Year 3 - 2s, 3s, 4s, 5s and 10s support multiples lists; dividing exactly vs remainder supports factors (Year 3 maths; AC Year 3).

Year 4–Year 5 - factor pairs, larger multiples, and light common-factor talk (Year 4; Year 5 maths).

Australian Curriculum Mathematics (v9) builds these through multiplication, division and number properties. At home: "Does 3 go into 12 with none left?" and "Can we skip-count by 4 to 20?" are enough.

Home games that do not feel like worksheets

Factor hunt. Pick 12 or 16. Build every array; write the factor pairs beside each.

Multiple hop. Skip-count by 3 or 5 along a hallway; ask whether a homework number lands on the path (skip counting).

Which word? Say "12 and 3" - is 3 a factor of 12, is 12 a multiple of 3, or both? (Both.) Celebrate the reasoning.

Odd/even factor chat. Even numbers always have factor 2; odd numbers do not (odd and even).

Story flip. Build 3 × 4 = 12; ask division "how many groups of 4 in 12?"

Keep games under ten minutes. If evenings fray - homework without tears, maths anxiety.

A simple weekly home routine

1. Two minutes of finding - one real equal-groups or array story with a small total (12, 16, 20).
2. Five minutes of naming - list factor pairs from the build; chant one multiples list (5s or 10s first).
3. Three minutes of contrasting - one "which word?" question (factor or multiple?) and optional common-factor share for two small numbers.

Stop while friendly. Frequency beats duration. For bare × fluency after meaning sits, use times tables without tears.

Common mix-ups (and kinder fixes)

Swapping factor and multiple. "Does 4 go into 12?" → 4 is a factor of 12. "Is 12 on the 4 skip-count?" → 12 is a multiple of 4. Same relationship, two directions.

Thinking every divisor with a remainder still "counts". Leftovers mean not a factor. Rebuild with counters until none are left - division.

Listing multiples by adding the wrong step. Multiples of 5 are not 5, 6, 7… Rebuild the skip-count hop (skip counting).

Rushing to long written lists before a picture. Arrays and equal groups first (arrays, equal groups); lists after the rectangles feel easy.

Treating this as a times-tables drill page. Fluency order lives on times tables explained and without tears. Wider foundation worry: Is my child behind in maths?.

How this links to other guides

• Multiplication explained for parents - umbrella × meaning and how siblings fit
• Equal groups explained for parents - piles / groups of as the core meaning zoom
• Arrays explained for parents - rows and columns; factor pairs as rectangles
• Times tables explained - three bridges into facts (overview)
• Times tables without tears - calm practice order once meaning is in place
• Skip counting explained - hops that are the multiples list
• Division explained - sharing and grouping; the "divides exactly" test
• Odd and even explained - light link to factor 2
• Year 2–Year 5 maths (Year 3, Year 4)
• Maths Help hub - more parent guides

Ask the teacher: "When homework says factors of 12, should we practise array rectangles and equal shares before writing the list - and how do you introduce multiples beside skip-counting?"

FAQ

What is a factor in primary maths?

A whole number that divides another whole number exactly (no remainder). The factors of 12 are 1, 2, 3, 4, 6 and 12.

What is a multiple?

A number you get by multiplying a whole number by 1, 2, 3… - the same sequence as skip-counting by that number. Multiples of 5 are 5, 10, 15, 20…

Are factors and multiples the same as times tables?

Related. Times-tables products are multiples; factor pairs are the two numbers you multiply to make a product. This page owns the factor/multiple words and contrast; fluency lives on the times-tables guides.

Do we need special materials?

No. Counters, Lego, pasta, scrap-paper rectangles and a skip-count chant are enough.

A calm next step

When factor pairs and multiples lists (and a confident "which word?") feel settled and you want a wider number-skill snapshot at home, Ziado's free check is a one-off, roughly 10-minute adaptive diagnostic with partial results only - no account and no card. The full placement unlocks after signup. It is not NAPLAN practice and it is not the full product; Ziado's ongoing path is adaptive maths (Foundation–Year 6) plus phonics reading (Foundation–Year 4). Explore Ziado maths if you want practice that can meet factors, multiples and related ×/÷ ideas at the right step. Individual and Family plans, if you continue later, start with a 14-day free trial of the full app — see pricing for current plans.

Remainder 0 means divides exactly — a light cousin of factors; leftovers live in remainders for parents.

Factors help estimate quotients in long division for parents.

Factors include n×n squares — see square numbers for parents.