Prime Factors and Triangular Numbers

The prime factorisation of a certain number is 3^{2} x 5 x 11.
 Write down the number.
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 Write down the prime factorisation of 165.
_________
 Write down the number.
_________

The first ten triangular numbers are:
1, 3, 6, 10, 15, 21, 28, 36, 45, 55
 From the list pick out all the multiples of 2.
6 10 28 36✓
 Pick out all the multiples of 3.
3 6 15 21 36 45✓
 Pick out any prime numbers.
3✓

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
 From the list pick out all the multiples of 2.
6 10 28 36✓

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.
 What is the volume (in cm3) of the wooden block?
_________
 What is the prime factorisation of the number found in part a)?
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 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.
_________
 What is the volume (in cm3) of the wooden block?
_________
 The prime factorisation of a certain number is 2' x 5 x 17.
 What is the number?
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 What is the prime factorisation of half of this number?
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 What is the prime factorisation of a quarter of the number?
_________
 What is the prime factorisation of an eighth of the number?
_________
 What is the number?
_________
 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?
_________
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