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Last Updated September 20, 2021, 10:24 am
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Prime Factors and Triangular Numbers

  1. The prime factorisation of a certain number is 32 x 5 x 11.
    1. Write down the number. _________
    2. Write down the prime factorisation of 165. _________

    Click your mouse on the question to answer, then click the maths symbol to add, but always use the keyboard if you can.

    ¼ ½ ¾ ÷ ì ² ³ 4 5 6 7 8 9 ƒ % x y z ( ) { } + - * / = ÷

  2. The first ten triangular numbers are: 1, 3, 6, 10, 15, 21, 28, 36, 45, 55
    1. From the list pick out all the multiples of 2. 6 10 28 36✓
    2. Pick out all the multiples of 3. 3 6 15 21 36 45✓
    3. Pick out any prime numbers. 3✓
    4. Add the numbers in the list together and write down the prime factorisation of the total.
      Triangle numbers can be doubled to make a rectangle, sometimes that helps you make a formula for sum of n triangular numbers. Eg 1 + 3 + 6 + 10 = 1/2 (11 * 5) where 5 is n , the number of triangular numbers.
      1 + 3 + 6 + 10
      10 + 6 + 3 + 1
      _________

    Click your mouse on the question to answer, then click the maths symbol to add, but always use the keyboard if you can.

    ¼ ½ ¾ ÷ ì ² ³ 4 5 6 7 8 9 ƒ % x y z ( ) { } + - * / = ÷

  3. Gordon is doing some woodwork and needs to calculate the volume of a wooden rectangular block (a cuboid). The length of the block is 50 cm, the height 25 cm and the width 16 cm.
    1. What is the volume (in cm3) of the wooden block? _________
    2. What is the prime factorisation of the number found in part a)? _________
    3. Gordon needs to cut the block into smaller blocks with dimensions 4 cm x 5 cm x 5 cm. What is the maximum number of small blocks Gordon can make from the larger block? Make sure you show all your working. _________

    Click your mouse on the question to answer, then click the maths symbol to add, but always use the keyboard if you can.

    ¼ ½ ¾ ÷ ì ² ³ 4 5 6 7 8 9 ƒ % x y z ( ) { } + - * / = ÷

  4. The prime factorisation of a certain number is 2' x 5 x 17.
    1. What is the number? _________
    2. What is the prime factorisation of half of this number? _________
    3. What is the prime factorisation of a quarter of the number? _________
    4. What is the prime factorisation of an eighth of the number? _________

    Click your mouse on the question to answer, then click the maths symbol to add, but always use the keyboard if you can.

    ¼ ½ ¾ ÷ ì ² ³ 4 5 6 7 8 9 ƒ % x y z ( ) { } + - * / = ÷

  5. Bryan and Sue were playing a guessing game. Sue thought of a number between 1 and 100 which Bryan had to guess. Bryan was allowed to ask five questions, which are listed with Sue's responses in the table below. Bryan's Questions Sue's Responses Is it prime? Is it odd? Is it less than 50? Is it a multiple of 3? Is it a multiple of 7? No No Yes Yes Yes What is the number that Sue thought of? _________ Start by writing down a number table up to 100. Look at each response in turn and cross off numbers until you've only got one left.
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