## All about Numbers

#### I love numbers. There is just so much to learn and explore. Click on the buttons below to learn more:

Even numbers are 2,4,6,8,10,12,14,16,….they are divisible by 2, i.e. you can share an even number of objects in to two equal piles of two.

Cuthbert and Betty are sharing 10 plums. Look at their plates, they have 5 plums each.

**Try sharing some different even numbers of plums or marbles at home.**

### Favourite numbers

#### My two favourite numbers are 144 and 6. Below, I explain why. As you study numbers more and more you will be able to understand everything that I write below.

### 144

This is a pretty amazing number…

It is very very square….

144 is a square number…

**144 = 12x12 = 12 ^{2}**

Each of its digits are also square numbers.

**1 = 1 ^{2} and 4 = 2^{2}**

Furthermore, the sum and product of its digits produce square numbers too.

**1 + 4 + 4 = 9 = 3 ^{2}**

and

**1 × 4 × 4 = 16 = 4**

^{2}

And (this is my favourite it), if you reverse the digits of 144 to 441 then you have another square number and not just any old square number either 21^{2} (21 being the reverse of 12)!

**441 = 21 ^{2}**

In addition to all of this, 144 is the 12^{th} term of the Fibonacci sequence:

The Fibonacci sequence is a recurrence relationship which means each new term is formed using one or more of the previous terms. In the case of the Fibonacci sequence, a term is formed by summing the previous two terms. The first two terms of the sequence must be defined before other terms can be generated. The first two terms of the Fibonacci sequence are 1 and 1. Then all the subsequence terms can be found.

### 6

6 Is the first perfect number…

Perfect numbers are numbers whose factors* (excluding themselves) add up to the number itself.

The factors of 6 (excluding 6) are 1, 2 and 3:

**1 + 2 + 3 = 6**

I like to think of six as ‘doubly’ perfect because the product of its factor (excluding 6) also make 6:

**1 × 2 × 3 = 6**

The first four perfect numbers are:

6, 28, 496, 8128

The factors of 28 (excluding 28) are 1, 2, 4, 7, 14:

**1 + 2 + 4 + 7 + 14 = 28**

The factors of 496 (excluding 496) are 1, 2, 4, 8, 16, 31, 62, 124, 248:

**1 + 2 + 4 + 8 + 16 + 31 + 62 + 124 + 248 = 496**

The factors of 8128 (excluding 8128) are 1, 2, 4, 8, 16, 32, 64, 127, 254, 508, 1016, 2032,4064:

**1 + 2 + 4 + 8 + 16 + 32 + 64 + 127 + 254 + 508 + 1016 + 2032 + 4064 = 8128**

Notice that they are all even. We do not know if any odd perfect numbers exist or how many such numbers exist or if there are an infinite number of perfect numbers.

*A factor is a number that divides into another number exactly without leaving a remainder. For example, 6 is a factor of 12 because 12 ÷ 6 = 2.

### What is your favourite number?

Why not tell me what your favourite number is and why. Look here each week to see if your work is uploaded.