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Even numbers

Any number that can be divided by \({2}\) is called an even number.

Some examples of even numbers are \({2}\), \({4}\), \({6}\), \({8}\), \({10}\), \({22}\), \({144}\) and \({2,020}\).

If a number ends with an even digit, then it is an even number. For example \({1~023~458}\) is even, because the final digit (\({8}\)) is even.

Odd numbers

Any number that cannot be divided by \({2}\) is called an odd number.

Some examples of odd numbers are \({1}\), \({3}\), \({5}\), \({7}\), \({9}\), \({35}\), \({177}\), \({2,435}\), etc.

If a number ends with an odd digit, then it is an odd number.

For example \({3~702~443}\) is odd, because the final digit (\({3}\)) is odd.

Square numbers

Square numbers are formed by multiplying a number by itself.

The first four square numbers are:

\(1 \times 1 = 1\)

\(2 \times 2 = 4\)

\(3 \times 3 = 9\)

\(4 \times 4 = 16\)

A shorthand way of writing a square number is to use the power \({2}\).

For example, \({3}\times{3}\) can be written as \({3}^{2}\).

Each square number can be represented as a square of dots:

Square numbers

Question

Write down the next six square numbers (from \({5}\) onwards). Then check your answer.

Cube numbers

Cube numbers are formed by multiplying a digit by itself three times.

For example, \(1\) cubed is \(1 \times 1 \times 1 = 1\)

\(2\) cubed is \(2 \times 2 \times 2 = 8\)

\(3\) cubed is \(3 \times 3 \times 3 = 27\)

\(4\) cubed is \(4 \times 4 \times 4 = 64\)

A shorthand way of writing a cube number is to use the power \({3}\).

For example, \({4}\times{4}\times{4}\) can be written as \({4}^{3}\).

Each cube number can be represented by a cube made up of unit cubes:

Cube numbers

Question

Use a calculator to find the next six cube numbers (from \({5}\) onwards) and then check your answer.

Triangle numbers

Triangle numbers can be represented as a triangle of dots.

The triangle numbers are:

Triangle numbers

Question

What is the next triangle number after \(21\)?

Multiples

The multiples of a number are those numbers that it will divide into exactly.

For example, the multiples of \({5}\) are \({5}\), \({10}\), \({15}\), \({20}\), \({25}\), \({30}\), \({鈥\)

Remember - multiples are like times tables:

  • \({1}\times{5} = {5}\)

  • \({2}\times{5} = {10}\)

  • \({3}\times{5} = {15}\)

  • \({4}\times{5} = {20}\)

Therefore, the multiples of \(5\) are \(5\), \(10\), \(15\), \(20\), \({鈥\)

Similarly the multiples of \({7}\) are \({7}\), \({14}\), \({21}\), \({28}\), \({35}\), \({42}\), \({鈥\)

Question

What are the first five multiples of \(11\)?

Test section

Question 1

Which of these is not an odd number?

a) \({17}\)

b) \({3,652,331,666,549}\)

c) \({574}\)

Question 2

What is the sixth even number?

a) \({12}\)

b) \({6}\)

c) \({10}\)

Question 3

Which of these is a square number?

a) \({32}\)

b) \({144}\)

c) \({40}\)

d) \({2}\)

Question 4

Which of these is a cube number?

a) \({1}\)

b) \({6}\)

c) \({9}\)

Question 5

Which of these is not a cube number?

a) \({64}\)

b) \({99}\)

c) \({1,000}\)

Question 6

Which of these is a triangle number?

a) \({15}\)

b) \({20}\)

c) \({25}\)

Question 7

Which of these is a square number and a triangle number?

a) \({55}\)

b) \({100}\)

c) \({36}\)

Question 8

What is the \({99}^{th}\) multiple of \({7}\)?

a) \({997}\)

b) \({693}\)

c) \({630}\)

Question 9

Which of the following numbers is a square number which is odd?

a) \({36}\)

b) \({111}\)

c) \({81}\)

Question 10

What's the first multiple of \({8}\) which is also a multiple of \({6}\)?

a) \({12}\)

b) \({48}\)

c) \({24}\)

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