Unknown factors/dividends/divisors | Year 5

01 / LEARN

Understand the idea.

Find a missing factor or dividend

A missing factor can be found by dividing the known product by the known factor. In $□ \times 8 = 96$ , ask how many groups of eight make $96$ . Since $96 \div 8 = 12$ , put $12$ in the square and check it.

A missing dividend is the total before division. In $□ \div 7 = 15$ , fifteen groups of seven rebuild that total, so use $15 \times 7 = 105$ . First locate the square: the operation you need depends on which number is missing.

Find a missing divisor

A missing divisor can be found with a related multiplication. In $84 \div □ = 7$ , use $7 \times □ = 84$ . The missing factor is $12$ , and $84 \div 12 = 7$ confirms its position in the original equation.

Substitute your answer back into the original sentence, not only the related fact. This helps distinguish a missing starting total from a missing group size or number of groups. Check that division never uses zero as the divisor.

Choose a related fact
Missing-number equation	Useful calculation	Check
□ × 8 = 96	96 ÷ 8 = 12	12 × 8 = 96
□ ÷ 7 = 15	15 × 7 = 105	105 ÷ 7 = 15
84 ÷ □ = 7	84 ÷ 7 = 12	84 ÷ 12 = 7

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Missing number of packs

Each pack holds twelve cards. There are 156 cards altogether. How many packs is this?

Worked solution

1
Represent the unknown number of packs.
$□ \times 12 = 156$
Each pack contributes 12 cards to the total of 156.
2
Use a nearby known product.
$12 \times 10 = 120, 156 - 120 = 36$
Ten packs account for 120 cards, leaving 36.
3
Count the extra packs.
$36 \div 12 = 3, 10 + 3 = 13$
The leftover cards make three more complete packs.
4
Substitute the pack count.
$13 \times 12 = 156$
The check accounts for all cards, so there are 13 packs.

Answer

13 packs.

EXAMPLE 02

Missing starting amount

Find the square in □ ÷ 9 = 24.

Worked solution

1
Identify the missing starting total.
$□ = 24 \times 9$
The dividend equals the quotient multiplied by the non-zero divisor.
2
Calculate the product in parts.
$24 \times 9 = (20 \times 9) + (4 \times 9) = 180 + 36$
Twenty-four groups of 9 split into twenty groups and four groups.
3
Find the missing number.
$180 + 36 = 216$
216 is the total before dividing by 9.
4
Check in the original equation.
$216 \div 9 = 24$
Substitution reproduces the required quotient.

Answer

216.

03 / YOUR TURN

Try it yourself.

Check your understanding

Find the square: 132 ÷ □ = 11.

Show answer & reasoning

12.

The related multiplication is $11 \times □ = 132$ . Since $11 \times 12 = 132$ , the missing divisor is $12$ ; $132 \div 12 = 11$ confirms it.

Keep practising

6 worksheet questions · 10 marks

Open worksheet Worked solutions

Read the questions online

Find the square: $□ \times 6 = 78$ .
1 mark
Find the square: $9 \times □ = 225$ .
1 mark
Find the square: $□ \div 8 = 17$ .
2 marks
Find the square: $144 \div □ = 12$ .
2 marks
A school shares an unknown number of books equally among seven classes. Each class receives 23 books. How many books were shared?
2 marks
A learner puts 48 in the square in $96 \div □ = 2$ . Is the answer correct? Show the original equation with the number substituted.
2 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

Find the square: $□ \times 6 = 78$ .
1 mark
$78 \div 6 = 13$ ; check $13 \times 6 = 78$ .
13.
Find the square: $9 \times □ = 225$ .
1 mark
$225 \div 9 = 25$ .
25.
Find the square: $□ \div 8 = 17$ .
2 marks
$17 \times 8 = 136$ ; check $136 \div 8 = 17$ .
136.
Find the square: $144 \div □ = 12$ .
2 marks
The related multiplication is $12 \times □ = 144$ .
12.
A school shares an unknown number of books equally among seven classes. Each class receives 23 books. How many books were shared?
2 marks
Write $□ \div 7 = 23$ .
Multiply $23 \times 7 = 161$ .
161 books.
A learner puts 48 in the square in $96 \div □ = 2$ . Is the answer correct? Show the original equation with the number substituted.
2 marks
Two groups of forty-eight make ninety-six.
The answer satisfies the original equation.
Yes: $96 \div 48 = 2$ .

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Curriculum reference & lesson scope

Australian Curriculum v9.0; SA Curriculum Mathematics 2026

One-/two-digit multipliers; division strategies; contextual remainders; inverse fact families; unknown factors/dividends/divisors.

Official curriculum source ↗

In this lesson

Understand the idea.

Find a missing factor or dividend

Find a missing divisor

See the method in action.

Missing number of packs

Represent the unknown number of packs.

Use a nearby known product.

Count the extra packs.

Substitute the pack count.

Missing starting amount

Identify the missing starting total.

Calculate the product in parts.

Find the missing number.

Check in the original equation.

Try it yourself.

Check your understanding

Keep practising