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Factors and multiples

Factors and multiples for GCSE Religious Studies AQA Higher: what it means, how to set the working out, and the questions it is asked in.
  • GCSE
  • AQA
  • Religious Studies
  • Higher
  • Spec N13 · N1
  • 14 min read
  • 9 revision boxes

Introduction

2 boxes
1 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.
Check the answer against an estimate before you move on, so a place-value slip is caught here.
Worth knowing: x2+5x+6=0x^2 + 5x + 6 = 0.
4 rows

The factors and multiples reference table

Work through the method one line at a time and write down what changes at each step.
Term
Meaning
Example
Row 1 column 1
Row 1 column 2
49=7\sqrt{49} = 7
Row 2 column 1
Row 2 column 2
a2+b2=c2a^2 + b^2 = c^2
Row 3 column 1
Row 3 column 2
49=7\sqrt{49} = 7
Row 4 column 1
Row 4 column 2
≈160\approx 160

Learning

5 boxes
3 steps

How to work with factors and multiples

The specification wording is precise here, and the mark scheme follows that wording exactly.
  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: a2+b2=c2a^2 + b^2 = c^2.
Answer: x2+5x+6=0x^2 + 5x + 6 = 0
3 rules

Key facts: Factors and multiples

Read the units in the question before you start; a converted unit is the most common slip.
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.
    a2+b2=c2a^2 + b^2 = c^2

  • Rule 3

    How factors and multiples behaves in the 3rd of the cases the specification names.
    ×10\times 10 moves every digit one column left
3 steps

How to work with factors and multiples

Check the answer against an estimate before you move on, so a place-value slip is caught here.
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.
  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.
Start from the definition and substitute the numbers the question gives you.
Simplify one line at a time: a2+b2=c2a^2 + b^2 = c^2.
Answer: 34×25\frac{3}{4} \times \frac{2}{5}
2 rules

Key facts: Factors and multiples

Work through the method one line at a time and write down what changes at each step.
Worth knowing: ≈160\approx 160.

  • Rule 1

    How factors and multiples behaves in the 1st of the cases the specification names.
    49=7\sqrt{49} = 7

  • Rule 2

    How factors and multiples behaves in the 2nd of the cases the specification names.
    ×10\times 10 moves every digit one column left

  • Rule 3

    How factors and multiples behaves in the 3rd of the cases the specification names.
    ×10\times 10 moves every digit one column left
3 steps

How to work with factors and multiples

The specification wording is precise here, and the mark scheme follows that wording exactly.
  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: 49=7\sqrt{49} = 7

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Examples

2 boxes
4 marks · worked

Worked example: factors and multiples

Read the units in the question before you start; a converted unit is the most common slip.
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.
1 marks · worked

Practice question 9: x2+5x+6=0x^2 + 5x + 6 = 0

Sketch the shape even when the question does not ask for one — it makes the next step obvious.

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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 GCSE Religious Studies AQA Higher paper?
Yes — it sits in the Ratio and proportion strand.