PAss Functional Skills

Factors and multiples

Factors and multiples for A Level Religious Studies AQA Higher: what it means, how to set the working out, and the questions it is asked in.
  • A Level
  • AQA
  • Religious Studies
  • Higher
  • Spec P10 · P14
  • 7 min read
  • 7 revision boxes

Introduction

2 boxes
3 min read

What is factors and multiples?

Listen to this box

Transcript

A short spoken summary of factors and multiples and where it is used.

A spoken walk-through of factors and multiples before you read the notes.
The examiner marks the working, so a correct answer with no method still drops marks.
2 rows

The factors and multiples reference table

This idea appears again in the higher-mark questions, so it is worth over-learning.
The layout below is the one the mark scheme expects.

Diagram showing factors and multiples laid out step by step

The same idea drawn out, so the method is visible.
Term
Meaning
Example
Common slip
Row 1 column 1
Row 1 column 2
≈160\approx 160
Row 1 column 4
Row 2 column 1
Row 2 column 2
x2+5x+6=0x^2 + 5x + 6 = 0
Row 2 column 4
Row 3 column 1
Row 3 column 2
≈160\approx 160
Row 3 column 4
Row 4 column 1
Row 4 column 2
×10\times 10 moves every digit one column left
Row 4 column 4

Learning

3 boxes
3 steps

How to work with factors and multiples

Sketch the shape even when the question does not ask for one — it makes the next step obvious.
The layout below is the one the mark scheme expects.

Diagram showing factors and multiples laid out step by step

The same idea drawn out, so the method is visible.
Worth knowing: a2+b2=c2a^2 + b^2 = c^2.
  1. Read the question and write down what is being asked for.
  2. Set out the working for factors and multiples in the order the method gives.
  3. Substitute the values and simplify.
  4. Check the answer against an estimate before writing it down.
Start from the definition and substitute the numbers the question gives you.
Simplify one line at a time: ≈160\approx 160.
Answer: x2+5x+6=0x^2 + 5x + 6 = 0
3 rules

Key facts: Factors and multiples

Practise the routine version until it is automatic, then move to the multi-step questions.
The layout below is the one the mark scheme expects.

Diagram showing factors and multiples laid out step by step

The same idea drawn out, so the method is visible.

  • Rule 1

    How factors and multiples behaves in the 1st of the cases the specification names.
    a2+b2=c2a^2 + b^2 = c^2

  • Rule 2

    How factors and multiples behaves in the 2nd of the cases the specification names.
    49=7\sqrt{49} = 7
3 steps

How to work with factors and multiples

The examiner marks the working, so a correct answer with no method still drops marks.
Worth knowing: 34×25\frac{3}{4} \times \frac{2}{5}.
  1. Read the question and write down what is being asked for.
  2. Set out the working for factors and multiples in the order the method gives.
  3. Substitute the values and simplify.
  4. Check the answer against an estimate before writing it down.
Start from the definition and substitute the numbers the question gives you.
Simplify one line at a time: x2+5x+6=0x^2 + 5x + 6 = 0.
Answer: ×10\times 10 moves every digit one column left

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Examples

2 boxes
1 marks · worked

Worked example: factors and multiples

The specification wording is precise here, and the mark scheme follows that wording exactly.
4 marks · worked

Practice question 7: 34×25\frac{3}{4} \times \frac{2}{5}

Sketch the shape even when the question does not ask for one — it makes the next step obvious.
Worth knowing: ≈160\approx 160.

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Common questions

How many marks is factors and multiples usually worth?
Between one and four, depending on how many steps the question asks for.
Is this on the A Level Religious Studies AQA Higher paper?
Yes — it sits in the Ratio and proportion strand.