IGCSEMathsEdexcelMaths BFlashcardsNumberPrime Factors, HCF & LCM

Prime Factors, HCF & LCM (Edexcel IGCSE Maths B): Flashcards

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  • FrontTypes of Number

    Define the term integer.

Cards in this collection (19)

  • Define the term integer.

    Integers are whole numbers. They can be positive, negative or zero.

  • What is a factor?

    A factor of a number is a positive integer that divides exactly into the number.

  • What is a multiple?

    A multiple of a number is a positive integer that can be made by multiplying the number by another integer.

  • Define a prime number.

    A prime number is a positive integer which has exactly two factors, itself and 1.

  • True or False?

    1 is a prime number.

    False.

    1 is not a prime number, as it only has one factor.

  • What is the only even prime number?

    2 is the only even prime number.

  • What are the first ten prime numbers?

    The first ten prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29.

  • What are the first twelve square numbers?

    The first twelve square numbers are: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144.

  • What are the first five cube numbers?

    The first five cube numbers are: 1, 8, 27, 64, 125.

  • True or False?

    Any positive integer has an infinite number of multiples.

    True.

    Any positive integer has an infinite number of multiples.

  • What is a natural number?

    A natural number is a positive integer.

    They are often referred to as counting numbers.
    Zero is not a natural number.

  • True or False?

    The result of any number multiplied by its reciprocal will be equal to 1.

    True.

    The result of any number multiplied by its reciprocal will be equal to 1.

    E.g. 3 cross times 1 third equals 1

  • What are prime factors?

    Prime factors of a number are the prime numbers which are factors of the number.

    E.g. 24 has the prime factors 2 and 3, (24 = 23 x 3)

  • What is prime factor decomposition?

    Prime factor decomposition (or Prime Factorisation) is the process of breaking a number up into its prime factors.

    Break a number into a pair of factors, then break those factors down in pairs in the same way until you are left with only prime factors.

    table row 72 equals cell 8 cross times 9 end cell row blank equals cell open parentheses 2 cross times 4 close parentheses cross times open parentheses 3 cross times 3 close parentheses end cell row blank equals cell 2 cross times open parentheses 2 cross times 2 close parentheses cross times 3 cross times 3 end cell row blank bold equals cell bold 2 bold cross times bold 2 bold cross times bold 2 bold cross times bold 3 bold cross times bold 3 end cell end table

  • How do you write a number as a product of prime factors?

    A product of prime factors can be found using prime factor decomposition then writing the prime factors of a number multiplied together.

    E.g. 36 equals 2 cross times 2 cross times 3 cross times 3 or 36 equals 2 squared cross times 3 squared.

  • True or False?

    500 can be written as a product of prime factors in the form 2 cross times 2 cross times 5 cross times 5 cross times 5.

    True.

    The prime factorisation of 500 equals 2 cross times 2 cross times 5 cross times 5 cross times 5.

    You may be asked to give your answer in the form 500 equals 2 squared cross times 5 cubed.

  • How can prime factor decomposition be used to identify if a number is a square number?

    To identify if a number is a square number, use prime factor decomposition.
    If the indices of all of its prime factors are even, the number is square.

    E.g. 36 is a square number: 36 equals 2 squared cross times 3 squared

    24 is not a square number: 24 equals 2 cubed cross times 3

  • True or False?

    You can identify a cube number by the fact that the index of each its prime factors is a cube.

    False.

    You can identify a cube number by the fact that the index of each of its prime factors is a multiple of 3.

    E.g. 216 is a cube number: 216 equals 2 cubed cross times 3 cubed

  • True or False?

    It can be shown, using its prime factors, that 10 square root of 15 is the exact square root of 1500.

    True.

    First write 1500 as a product of its prime factors, e.g. 1500 equals 2 squared cross times 3 cross times 5 cubed

    Separate prime factors with an even index and those with an odd index, e.g. 1500 equals open parentheses 2 squared cross times 5 squared close parentheses cross times open parentheses 3 cross times 5 close parentheses

    Take the square root of both groups,
    e.g. table row cell square root of 1500 end cell equals cell square root of open parentheses 2 squared cross times 5 squared close parentheses end root cross times square root of open parentheses 3 cross times 5 close parentheses end root end cell row blank equals cell 2 cross times 5 cross times square root of 15 end cell row blank equals cell 10 square root of 15 end cell end table

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