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Maths Gcse Aqa Higher

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  1. Scatter-Graphs-And-Correlation Aqa Higher
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  4. Statistical-Diagrams Aqa Higher
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  32. Real-Life-Graphs Aqa Higher
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  35. Functions Aqa Higher
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  37. Graphs-Of-Functions Aqa Higher
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  38. Linear-Graphs Aqa Higher
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  44. Algebraic-Proof Aqa Higher
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  48. Factorising Aqa Higher
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  55. Introduction Aqa Higher
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  58. Fractions Aqa Higher
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  59. Powers-Roots-And-Standard-Form Aqa Higher
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  61. Number-Operations Aqa Higher
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Exam code:8300

Prime factor decomposition

What are prime factors?

  • A factor of a given number is a value that divides the given number exactly, with no remainder

    • e.g. 6 is a factor of 18

  • A prime number is a number which has exactly two factors; itself and 1

    • e.g. 5 is a prime number, as its only factors are 5 and 1

    • You should remember the first few prime numbers:

      • 2, 3, 5, 7, 11, 13, 17, 19, …

  • The prime factors of a number are therefore all the primes which multiply to give that number

    • e.g. The prime factors of 30 are 2, 3, and 5

      • 2 × 3 × 5 = 30

How do I find prime factors?

  • Use a factor tree to find prime factors

    • Split the number up into a pair of factors

    • Then split each of those factors up into another pair

    • Continue splitting up factors along each “branch” until you get to a prime number

      • These can not be split into anything other than 1 and themselves

      • It helps to circle the prime numbers at the end of the branches

Prime factors of 360 in a factor tree

  • A number can be uniquely written as a product of prime factors

    • Write the prime factors as a multiplication, in ascending order

      • 360 = 2 × 2 × 2 × 3 × 3 × 5

    • This can then be written more concisely using powers

      • 360 = 23 × 32 × 5

  • A question asking you to do this will usually be phrased as “Express … as the product of its prime factors”

Worked Example

Write 432 as the product of its prime factors.

Create a factor tree
Start with 432 and choose any two numbers that multiply together to make 432

igcse-core-maths-oct-19-paper-3-q4g-1

Repeat this for the two factors, until all of the values are prime numbers and cannot be broken down any further

igcse-core-maths-oct-19-paper-3-q4g-2

The answer will be the same regardless of the factors chosen in the first step

Write the prime numbers out as a product

432 equals space 2 space cross times space 2 space cross times space 2 space cross times space 2 space cross times space 3 space cross times space 3 space cross times space 3

Any repeated prime factors can be written as a power

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