GCSE Maths Practice: factors-and-multiples

Question 8 of 10

This GCSE Maths question checks your understanding of multiples. You’ll need to identify which of the given options appears in the 7 times table.

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\( \begin{array}{l}\text{Which of the following numbers is a multiple of 7?}\end{array} \)

Choose one option:

To check for a multiple, divide by the base number or list its times table. If the result is a whole number, that option is correct.

Understanding Multiples

Multiples are the numbers you get when you multiply a number by 1, 2, 3, 4, and so on. They form the times table of that number. For example, the multiples of 7 are 7, 14, 21, 28, 35, 42, 49, and so on. Knowing how to find and recognise multiples is a key part of the GCSE Maths Number topic.

Multiples are useful for finding the Lowest Common Multiple (LCM), working with fractions, and solving problems that involve equal groups, patterns, or repeated addition.

How to Identify a Multiple

  1. List the first few multiples of the number by multiplying it by 1, 2, 3, etc.
  2. Compare each option in the question to that list.
  3. If one of the options appears in the list, it is a multiple.
  4. Alternatively, divide the number by the base number — if the result is a whole number, it is a multiple.

Worked Examples (Different Values)

  • Example 1: Which of the following is a multiple of 6: 17, 24, 25?
    24 ÷ 6 = 4 → exact → 24 is the multiple of 6.
  • Example 2: Which of these is a multiple of 8: 30, 40, or 42?
    40 ÷ 8 = 5 → exact → 40 is the multiple.
  • Example 3: Which is a multiple of 9: 54, 56, or 58?
    54 ÷ 9 = 6 → exact → 54 is the multiple.

Difference Between Multiples and Factors

  • Factors divide a number exactly (they go into it).
  • Multiples are the results of multiplying the number (they go beyond it).

For example, for 7: factors are 1 and 7, while multiples are 7, 14, 21, 28, and so on.

Common Mistakes

  • Forgetting to multiply correctly: Skipping steps or miscalculating can lead to wrong answers.
  • Confusing factors and multiples: Factors are smaller or equal to the original number; multiples are equal or larger.
  • Assuming consecutive numbers are multiples: Multiples of a number increase by regular intervals, not by 1 each time.

Real-Life Applications

Multiples are used in scheduling, packaging, and grouping problems. For example, if buses leave every 7 minutes, their departure times (0, 7, 14, 21, 28, etc.) are multiples of 7. Similarly, when making equal groups in design, stock, or data batching, multiples help ensure fair distribution.

In technology and coding, multiples help align data intervals and repeat tasks in loops — an essential concept in computer science and algorithm design.

Frequently Asked Questions

Q1: Can zero be a multiple of a number?
A: Yes, zero is a multiple of every number because any number multiplied by 0 equals 0.

Q2: What is the smallest multiple of any number?
A: The smallest multiple is the number itself (for example, 7 × 1 = 7).

Q3: How do multiples help find the LCM?

A: The LCM (Lowest Common Multiple) is the first number that appears in both multiplication lists of two or more numbers.

GCSE Study Tip

When checking options, divide each by the base number. If you get a whole number, it’s a multiple. If not, cross it off. Writing out the first six multiples of common numbers like 2, 3, 4, 5, 6, 7, 8, 9 is great practice for quick recall in exams.

Summary

Multiples are key to understanding number patterns and divisibility. To identify them, multiply or divide to see if a number fits exactly. The correct answer in this question is 28, as it appears in the 7 times table. Mastering this topic builds the foundation for LCM, ratios, and arithmetic fluency in GCSE Maths.