## Understanding Math integers for Pre-algebra number work

Math integers and number work is one of those unnecessary topics we need to know about for pre algebra. We sort of need it, but then again we could get away with out knowing them.

I know I have contradicted myself twice here, but my point is that most of these are either common sense (self explanatory) or you already know them from primary school.

Math integers are basically all maths work that involve number work. The word math integers is a fancy mathematical word that means number.

We will start each one with a definition of it and then give an example or two.

**1. Odd numbers** – An odd number or if you would like to use the fancy name 'math integers', is a number that cant be divided by two. All odd numbers end with 1, 3, 5, 7 or 9. For example, 19, 23 and -105 are odd numbers.

(This next bit may go over the head a little, like...whoosh!) but stay with us, here we go

Using algebra, if n is a whole number then this thing 2n+1 is always odd.

For example, when we put numbers into n, n=1, then the answer is 2(1)+1=3

If we put 2 into n, n=2, then the answer is 5, 2(2)+1=5

and so on

2. **Even numbers** - A number or math integers that has a factor of two is called an even number.

An even number always ends in 0, 2, 4, 6 or 8. Even numbers are multiples of 2, 4, 6, 8, 10, 12 …

3. **Multiples** - A multiple is a number when another number divides exactly into it.

For example 5, 10, 15, 20, 25...are all multiples of 5. Note all numbers are multiples of 1.

4. **Factors** - A number/integer which divides exactly into another number is called a factor. 1, 2, 5 and 10 are the factors of 10.

Basically, those numbers go into or divide exactly into 10.

factors of 12 are 1, 2, 3, 4, 6 and 12

factors of 17 are 1 and 17

factors of 32 are 1, 2, 4, 8, 16 and 32

5. **Highest common factor** - the largest factor shared by two numbers is their highest common factor (or HCF).

The HCF of 18 and 24 is 6. First look for all the factors of 18. They are 1, 2, 3, 6,9 and 18. Then find the factors of 24 which are 1, 2, 3, 4, 6, 8, 12 and 24. The highest number in both groups is 6.

More examples:

the HCF of 6, 8, and 12 is 2

the HCF of 20 and 45 is 5

the HCF of 42 and 56 is 14

6. **Prime numbers** - A prime number has only two factors, itself and 1. There are an infinite number of prime numbers.

For example 2, 3, 5, 7, 11, 13, 17, 19 etc.

Note : 2 is the only even prime number and 1 is not a prime number.

The factors of 12 are 1, 2, 3, 4, 6, 12. So, 2 and 3 are prime factors of 12.

The factors of 16 are 1, 2, 4, and 8. Then 2 is the prime factor of 16.

24 as a product of prime factors is 2×2×2×3

How did that happen? 24 breaks down into 2 and 12. 2 does not break down anymore but 12 does.

12 breaks down into 2 and 6. Then break 6 down again to give 2 and 3.

Finally, gather up all the numbers that stopped breaking down along the chain to give 2×2×2×3

7. **Square numbers** - these numbers are 1, 4, 9, 16, 25, 36, 49, 64, …

We got these numbers by multiplying a number by itself 1×1, 2×2, 3×3, 4×4, …

So, to find the fifth square number we multiply 5 by itself, to give 25.

8. **Triangle numbers** - these numbers are 1, 3, 6, 10, 15, …

Lets see if you can spot the pattern in finding triangle numbers.

1=1

1+2=3

1+2+3=6

1+2+3+4=10

1+2+3+4+5= ?

9. **Integer** - An integer is a whole number such as 0, 1, 2, 3, 4...

They can also include negative numbers such as -1, -2, -3...

At this point we should provide some questions and answers, trust me we will provide them in due course.

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