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**Working with Number Example: 6, 12, 18 and 24 are all multiples of 6**

Multiples of a number are the result of multiplying that number by other WHOLE numbers !!! Example: 6, 12, 18 and 24 are all multiples of 6

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Factors of a number are whole numbers that can be divided into that number with other whole numbers as a result !! Example: 1 and 12 2 and 6 3 and 4 Are all factors of 12, since if the pairs are multiplied together, they will equal 12

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**A Prime Number has only TWO FACTORS, itself and one.**

Example: 2, 3, 5, 7, 11, 13 are Prime Numbers because only 1 and the actual number are factors. What other prime numbers less than 50 are there? NOTE: 1 is not a prime number because it has only ONE FACTOR!! 4, 8 and 9 are not prime numbers because they have other factors besides 1 and the number !!!

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Prime Factors of a number are the numbers that are factors of the number itself and are themselves prime numbers. The Factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. BUT only 2 and 3 are prime numbers, so the prime factors of 24 are 2, and 3. To find prime factors you divide by the prime numbers in order; (2 until you cannot divide further, then 3, etc)

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**To find the prime factors of 24**

Divide by ÷ 2 = 12 Divide by ÷ 2 = 6 Divide by ÷ 2 = 3 Divide by ÷ 3 = 1 So the prime factors of 24 are: 2 x 2 x 2 x 3 or 23 x 3

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**Another way to find prime factors is to use a “Factor Tree”.**

As before you divide the number being tested by 2, 3, 5 etc having the prime factors on one series of branches and the resultant numbers on the other. See next slide for details

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**Find the prime factors of 54**

Using a factor tree 2 27 The numbers along this line are the factors of 54 9 3 3 3 So, the factors of 54 are 2 x 3 x 3 x 3 or 2 x 33

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Least Common Multiple (LCM) of two numbers is the smallest number that is a multiple of both numbers. It is not necessarily the simple multiple of the numbers. For example the least Common Multiple of 4 and 6 is 12. More on this later

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Highest Common Factor (HCF) of two numbers is the largest number that is a factor to both the given numbers. More on this a bit later

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**Square Root (√) of a number is the reverse of the above. **

A Square Number is a number that has A SQUARED number as a factor. E.g. 9 = being a Square Number. As are 1, 4, 16, 25, etc. Square Root (√) of a number is the reverse of the above. E.g. √16 = 4, 4 is the square root of 16, similarly √9 = 3; √4 = 2; √25 = 5

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**Numbers raised to the power of 3 result in Cube Numbers. E. g**

Numbers raised to the power of 3 result in Cube Numbers. E.g. 33 = 3 x 3 x 3 = 27 and = 4 x 4 x 4 = 64. So 27 and 64 are Cube Numbers (they are the result of a number cubed!!! You need to understand FULLY how your calculator works in working out squares, square roots, cubes and cube roots. PRACTISE!!!

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**POWERS of numbers is where the number is raised to another number**

POWERS of numbers is where the number is raised to another number. This involves using the xy button on your calculator (mobile phones rarely have this facility!!!!) The other way you can work it out is to do multiple multiplications (quite tedious and can lead to mistakes)!!! E.g. 37 = 3 x 3 x 3 x 3 x 3 x 3 x 3 = 3 xy 7 = 2187 In entering 3 x 3 x 3 x 3 x 3 x 3 x 3 = you can easily miscount !!!

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When multiplying and dividing numbers raised to powers, providing the BASE number is the same, multiplying means you ADD the powers and dividing means you subtract the powers. E.g. 86 x 83 = 86+3 = 89

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If base numbers are different or the numbers are to be added or subtracted, you have to do things the hard way (work them out) E.g. 43 x 36 Base numbers are different (4 and 3) therefore you need to work out the powers individually and then add the results!! 43 x 36 = 4 x 4 x 4 x 3 x 3 x 3 x 3 x 3 x 3 = 64 x 729 = 46656

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**You can also use the button on your calculator.**

Reciprocal of a number is one divided by that number. E.g. Reciprocal of 4 is (1/4) = 1 4 = 0.25 Reciprocal of 28 = 1 28 = …. You can also use the button on your calculator. Find it and know how to use it!!

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