Presentation on theme: "Working with Number Example: 6, 12, 18 and 24 are all multiples of 6"— Presentation transcript:
1Working 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
2Factors of a number are whole numbers that can be divided into that number with other whole numbers as a result !!Example: 1 and 122 and 63 and 4Are all factors of 12, since if the pairs are multiplied together, they will equal 12
3A 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 !!!
4Prime 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)
5To find the prime factors of 24 Divide by ÷ 2 = 12Divide by ÷ 2 = 6Divide by ÷ 2 = 3Divide by ÷ 3 = 1So the prime factors of 24 are:2 x 2 x 2 x 3 or 23 x 3
6Another 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
7Find the prime factors of 54 Using a factor tree227The numbers along this line are the factors of 549333So, the factors of 54 are 2 x 3 x 3 x 3 or 2 x 33
8Least 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
9Highest 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
10Square 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
11Numbers 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!!!
12POWERS 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 = 2187In entering 3 x 3 x 3 x 3 x 3 x 3 x 3 = you can easily miscount !!!
13When 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
14If 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 36Base 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
15You 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 = 0.25Reciprocal of 28 = 1 28 = ….You can also use the button on your calculator.Find it and know how to use it!!