All about Numbers

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

Even

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.

Odd

Odd numbers are 1,3,5,7,9,11,13,15,….they are not divisible by two. When you try to share them in to two equal piles, there will always be one left over.

Cuthbert and Betty are sharing 9 plums. Look at their plates, they have four each and there is one left over – can you think of what they could do to share this 1 equally?

Try sharing some different odd numbers of plums or marbles at home. Can you explain why there is always 1 left over when you share them out equally?

Prime

Prime numbers are numbers that are only divisible by 1 and themselves. The first few prime numbers are 2,3,5,7,11, can you work out anymore?

The trick is to find numbers that do not appear in the timetables of any other numbers. For example, 15 is not prime because it appears in the 3 times table.

Did you know that 2 is the only even prime number? Do you know why this is? Click here to check you answer

Step

Square

Cube

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 = 12²

Each of its digits are also square numbers.

1 = 1² and 4 = 2²

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

1 + 4 + 4 = 9 = 3²
and
1 × 4 × 4 = 16 = 4²

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 21² (21 being the reverse of 12)!

441 = 21²

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.