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Maths Gcse Edexcel Higher

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  1. Scatter-Graphs-And-Correlation Edexcel Higher
    2 主题
  2. Cumulative-Frequency-And-Box-Plots Edexcel Higher
    4 主题
  3. Histograms Edexcel Higher
    3 主题
  4. Statistical-Diagrams Edexcel Higher
    7 主题
  5. Averages-Ranges-And-Data Edexcel Higher
    8 主题
  6. Combined-And-Conditional-Probability Edexcel Higher
    3 主题
  7. Tree-Diagrams Edexcel Higher
    1 主题
  8. Simple-Probability-Diagrams Edexcel Higher
    3 主题
  9. Transformations Edexcel Higher
    5 主题
  10. Vectors Edexcel Higher
    6 主题
  11. 3D-Pythagoras-And-Trigonometry Edexcel Higher
    1 主题
  12. Sine-Cosine-Rule-And-Area-Of-Triangles Edexcel Higher
    4 主题
  13. Pythagoras-And-Trigonometry Edexcel Higher
    4 主题
  14. Area-And-Volume-Of-Similar-Shapes Edexcel Higher
    1 主题
  15. Congruence-Similarity-And-Geometrical-Proof Edexcel Higher
    5 主题
  16. Volume-And-Surface-Area Edexcel Higher
    3 主题
  17. Circles-Arcs-And-Sectors Edexcel Higher
    2 主题
  18. Area-And-Perimeter Edexcel Higher
    4 主题
  19. Circle-Theorems Edexcel Higher
    7 主题
  20. Bearings-Scale-Drawing-Constructions-And-Loci Edexcel Higher
    5 主题
  21. Angles-In-Polygons-And-Parallel-Lines Edexcel Higher
    3 主题
  22. Symmetry-And-Shapes Edexcel Higher
    6 主题
  23. Exchange-Rates-And-Best-Buys Edexcel Higher
    2 主题
  24. Standard-And-Compound-Units Edexcel Higher
    5 主题
  25. Direct-And-Inverse-Proportion Edexcel Higher
    2 主题
  26. Problem-Solving-With-Ratios Edexcel Higher
    2 主题
  27. Ratios Edexcel Higher
    3 主题
  28. Sequences Edexcel Higher
    4 主题
  29. Transformations-Of-Graphs Edexcel Higher
    2 主题
  30. Graphing-Inequalities Edexcel Higher
    2 主题
  31. Solving-Inequalities Edexcel Higher
    2 主题
  32. Real-Life-Graphs Edexcel Higher
    4 主题
  33. Estimating-Gradients-And-Areas-Under-Graphs Edexcel Higher
    2 主题
  34. Equation-Of-A-Circle Edexcel Higher
    2 主题
  35. Graphs-Of-Functions Edexcel Higher
    6 主题
  36. Linear-Graphs Edexcel Higher
    4 主题
  37. Coordinate-Geometry Edexcel Higher
    4 主题
  38. Functions Edexcel Higher
    3 主题
  39. Forming-And-Solving-Equations Edexcel Higher
    3 主题
  40. Iteration Edexcel Higher
    1 主题
  41. Simultaneous-Equations Edexcel Higher
    2 主题
  42. Quadratic-Equations Edexcel Higher
    4 主题
  43. Linear-Equations Edexcel Higher
    1 主题
  44. Algebraic-Proof Edexcel Higher
    1 主题
  45. Rearranging-Formulas Edexcel Higher
    2 主题
  46. Algebraic-Fractions Edexcel Higher
    4 主题
  47. Completing-The-Square Edexcel Higher
    1 主题
  48. Factorising Edexcel Higher
    6 主题
  49. Expanding-Brackets Edexcel Higher
    3 主题
  50. Algebraic-Roots-And-Indices Edexcel Higher
    1 主题
  51. Introduction Edexcel Higher
    7 主题
  52. Using-A-Calculator Edexcel Higher
    1 主题
  53. Surds Edexcel Higher
    2 主题
  54. Rounding-Estimation-And-Bounds Edexcel Higher
    2 主题
  55. Fractions-Decimals-And-Percentages Edexcel Higher
    3 主题
  56. Simple-And-Compound-Interest-Growth-And-Decay Edexcel Higher
    4 主题
  57. Percentages Edexcel Higher
    3 主题
  58. Fractions Edexcel Higher
    4 主题
  59. Powers-Roots-And-Standard-Form Edexcel Higher
    4 主题
  60. Prime-Factors-Hcf-And-Lcm Edexcel Higher
    4 主题
  61. Number-Operations Edexcel Higher
    10 主题
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Exam code:1MA1

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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