Number – relationships

Number - Relationships

Number relationships All numbers have relationships, with other numbers.

For example 6 is 6; but is it also 3 x 2, 6 x 1, half of 12, it can be divided equally.

Multiples Multiples The multiples of a number are the numbers in the multiplication table.

The multiples of 3 are all the numbers in the 3 times table.

To check if a number is a multiple of 3, divide it by 3 and make sure there are no remainders.

Common Multiples Common multiples are numbers that occur in multiple tables.

For example 12 is a common multiple of 3 and 4 3, 6, 9, 12 4, 8, 12, 16

Factors The factors of a number are all the numbers that divide into it exactly, leaving no remainder.

Find the factors of 6 6 รท 3 = 2so

3 is a factor

6 รท 2 = 3so

3 is a factor

6 รท 6 = 1so

6 is a factor

6 รท 1 = 6so

1 is a factor

All the factors of 6 are 1, 2, 3 and 6 You can write factors in pairs. The factor pairs are: (6, 1) 6 x 1 = 6 (2, 3) 2 x 3 = 6 Factors of even numbers can be odd or even, but factors of odd numbers are always odd numbers.

You can divide 1 and itself, so all numbers have at least two factors.

Even and Odd Even numbers An even number is any multiple of 2. so all whole numbers that can be divided by 2 to give a whole number are EVEN. If a number ends in 2, 4, 6, 8, or 0 it is even. Zero is considered to be an even number.

This works for negative numbers as well, so - 2, - 48 and - 556 are all even numbers.

The first five even numbers greater than zero are 2, 4, 6, 8, 10 Odd numbers Any number that is not a multiple of 2 is an odd number. So all whole numbers that cannot be divided by 2 to give a whole number are ODD. An easy way to spot odd numbers is to remember that they all end in 1, 3, 5, 7, or 9.

So 5, 51 and 463 are all odd numbers. This works for negative numbers too. - 5, - 51 and – 463 are all odd numbers.

The first five positive odd numbers are 1, 3, 5, 7, 9

Composite Numbers A composite number has three or more factors.

For example, 10 has four factors: 1, 2, 5 and 10 Except for 2, all even numbers are composite. Every number greater than 1 is either a prime number or a composite number.

Prime Numbers If a number only has 1 and itself as a factor, we call it a prime number.

The first positive ten prime numbers are: 2 3 5 7 11 13 17 19 23 29 Here are some useful hints to remember about prime numbers: 1 is not a prime number because it has only one factor: 1 2 is the only even prime number All the others are odd numbers Except for 2 and 5, all prime numbers end in 1, 3, 7 or 9 (but not all numbers that end in 1, 3, 7, 9 are prime).

Square Numbers When a number is multiplied by itself, it is known as the square of the number. For example, multiplying 4 by itself gives the square number 16 .

Square numbers are numbers that make squares. as 22 = 4

2 x 2 can be written

Triangular Numbers If you add consecutive numbers from 1, you get triangular numbers. These can be shown as a triangular pattern of dots. The last row of dots is one dot longer each time.

Cube Numbers Any number multiplied by itself and then by itself again is a cube number.

For example 2 x 2 x 2 = 8 The first ten cube numbers are 8 27 64 125 216 343 512 729 1000 Tip – the cube of an even number is always even and the cube of an odd is always odd.

Exploring Number Patterns • 2, 6, 10,... is a number pattern that follows the rule 'add 4' • The next number is 10 + 4 = 14 • 81, 27, 9, .... is a number pattern that follows the rule 'divide by 3' • The next number is 9 ÷ 3 = 3 • 5, 8, 14, ... is a number pattern that follows the rule 'subtract 1, multiply by 2' • The next number is (14 -1) × 2 = 26 • Each number in a number pattern is called a term. So in the number pattern 2, 6, 10 ... the first term is 2, the second term is 6 and the third term is 10

Fibonacci Sequence • The Fibonacci Sequence is the series of numbers: • 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ...

• The next number is found by adding up the two numbers before it • The 2 is found by adding the two numbers before it (1+1) • Similarly, the 3 is found by adding the two numbers before it (1+2) • And the 5 is (2+3) • and so on!

• Example: the next number in the sequence above is 21+34 = 55

Pascal’s Triangle One of the most interesting Number Patterns is Pascal's Triangle (named after Blaise Pascal, a famous French Mathematician and Philosopher).

To build the triangle, start with "1" at the top, then continue placing numbers below it in a triangular pattern.

Each number is the numbers directly above it added together.

(Here I have highlighted that 1+3 = 4)