Number+Patterns+-+Louise

== = WELCOME, You have arrived at the page dedicated to Whole Number Patterns. This page is created by Louise Drury!! =

2.1 MULTIPLES and FACTORS!!
The __//multiples//__ of a number are the products of that number and any other number you wish. of 6 are:
 * = **EXAMPLE** ||=  **EXPLANATION**  ||
 * = The multiples
 * 6, 12, 18, 24, 30.** ||=  6x1=**6** 6x2=**12** 6x3=**18** 6x4=**24** 6x5=**30**   ||

The __//factors//__ of a number are numbers that can be multiplied together to equal the original number. 64x1=64 2x32=64 16x4=64 || **NOTE-** LCM means Lowest Common Multiple, HCF means Highest Common Factor, ect. 2.1 Questions?? Q.1 Write the first three common multiples of 6 and 7?? Q.2 List the factor pairs of 46?? Q.3 What is the lowest and highest factor any number can have??
 * **EXAMPLE** || **EXPLANATION**  ||
 * The factors of 64 are: **64,1,8,2,32,16,4** || 8x8=64

2.2 PRIME and COMPOSITE numbers!!
<span style="color: #000080; font-family: 'Comic Sans MS',cursive; font-size: 130%;">All numbers except for 1 are considered to be prime or composite numbers.

<span style="color: #000080; font-family: 'Comic Sans MS',cursive; font-size: 120%;">__//Prime numbers//__ only have two factors; one and itself! <span style="color: #000080; font-family: 'Comic Sans MS',cursive; font-size: 120%;">//__Composite numbers__// have more than two factors E.G. 49 is composite because is has 3 factors; 49, 1, & 7 <span style="color: #000080; font-family: 'Comic Sans MS',cursive; font-size: 120%;">This table shows all the prime numbers(white) and composite numbers (green) up to 100. <span style="color: #000080; font-family: 'Comic Sans MS',cursive; font-size: 120%;">The number one is blue because it is neither!

<span style="color: #fd0057; font-family: Georgia,serif; font-size: 150%;">2.2 Questions?? <span style="color: #000080; font-family: 'Comic Sans MS',cursive; font-size: 120%;">Q.1 How many prime numbers are there betweeen 1 to 100?? <span style="color: #000080; font-family: 'Comic Sans MS',cursive; font-size: 120%;">Q.2 How many even prime numbers are there, what are they and why is this?? <span style="color: #000080; font-family: 'Comic Sans MS',cursive; font-size: 120%;">Q.3 Work out how many prime nubers there are between 1 & 50. Then work out how many there are between 50 & 100. <span style="color: #000080; font-family: 'Comic Sans MS',cursive; font-size: 120%;">Which group contains more prime numbers??

[|Chapter 2.1-2.4 ANSWERS!!.docx]

<span style="color: #00ff00; font-family: Georgia,serif; font-size: 210%;">2.3 DIVISIBILITY of LARGE NUMBERS!!
<span style="color: #000080; font-family: 'Comic Sans MS',cursive; font-size: 130%;">It can be very useful to know quickly if a number is evenly divisible by another!


 * = <span style="color: #00a7ff; font-family: 'Arial Black',Gadget,sans-serif; font-size: 200%;">A NUMBER ||= <span style="color: #00a7ff; font-family: 'Arial Black',Gadget,sans-serif; font-size: 200%;">IS EXACTLY  ||= <span style="color: #00a7ff; font-family: 'Arial Black',Gadget,sans-serif; font-size: 200%;">DIVISIBLE BY  ||
 * <span style="color: #ff8400; display: block; font-family: Impact,Charcoal,sans-serif; font-size: 250%; text-align: center;">2 || <span style="color: #ff8400; display: block; font-family: Impact,Charcoal,sans-serif; font-size: 250%; text-align: center;">3 || <span style="color: #ff8400; display: block; font-family: Impact,Charcoal,sans-serif; font-size: 250%; text-align: center;">4 ||
 * <span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: center;">If it ends in <span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: center;">0, 2, 4, 6 or 8. || <span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: center;">If the sum of its digits is  <span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: center;">divisible by 3. || <span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: center;">If the last 2 digits are  <span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: center;">divisible by 4. ||
 * <span style="color: #ff8400; display: block; font-family: Impact,Charcoal,sans-serif; font-size: 250%; text-align: center;">5 || <span style="color: #ff8400; display: block; font-family: Impact,Charcoal,sans-serif; font-size: 250%; text-align: center;">6 || <span style="color: #ff8400; display: block; font-family: Impact,Charcoal,sans-serif; font-size: 250%; text-align: center;">7 ||
 * <span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: center;">If the last digit is a5 or 0. || <span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: center;">If it is divisible by both  <span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: center;">2 and 3. || <span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: center;">There is no quick test for 7!  ||
 * <span style="color: #ff8400; display: block; font-family: Impact,Charcoal,sans-serif; font-size: 250%; text-align: center;">8 || <span style="color: #ff8400; display: block; font-family: Impact,Charcoal,sans-serif; font-size: 250%; text-align: center;">9 || <span style="color: #ff8400; display: block; font-family: Impact,Charcoal,sans-serif; font-size: 250%; text-align: center;">10 ||
 * If the last 3 digits are divisible by 8. || If the sum of its digits is divisible by 9. || if it ends in 0 ||

<span style="color: #ff0057; font-family: Georgia,serif; font-size: 150%;">2.3 Questions?? <span style="color: #000080; font-family: 'Comic Sans MS',cursive; font-size: 120%;">Q.1 What is the first whole number that is divisible by 5, 10 & 8?? <span style="color: #000080; font-family: 'Comic Sans MS',cursive; font-size: 120%;">Q.2 Choose any 4 digit number with 4 different digits, What is is exactly divisible by?? <span style="color: #000080; font-family: 'Comic Sans MS',cursive; font-size: 120%;">Q.3 Is 7628 evenly divisible by 6, 8 and 2??

<span style="color: #00ff00; font-family: Georgia,serif; font-size: 210%;">2.4 MULTIPLICATION STRATEGIES!!
<span style="color: #000080; font-family: 'Comic Sans MS',cursive; font-size: 130%;">To be able to perform mental calculations with multiplication is very useful.

<span style="color: #000080; font-family: 'Comic Sans MS',cursive; font-size: 120%;">In multiplication numbers can be __//multiplied in any order//__ and you will still get the same result. <span style="color: #000080; font-family: 'Comic Sans MS',cursive; font-size: 120%;">This can be useful to make calculations easier. <span style="color: #000080; font-family: 'Comic Sans MS',cursive; font-size: 130%;">Some other strategies include- <span style="color: #000080; font-family: 'Comic Sans MS',cursive; font-size: 120%;">Rounding decimals (for estimations) <span style="color: #000080; font-family: 'Comic Sans MS',cursive; font-size: 120%;">Doubling and halving <span style="color: #000080; font-family: 'Comic Sans MS',cursive; font-size: 120%;">Look for numbers that give 100 (25x 4)
 * <span style="color: #00a7ff; font-family: 'Arial Black',Gadget,sans-serif; font-size: 200%;"> EXAMPLE || <span style="color: #00a7ff; font-family: 'Arial Black',Gadget,sans-serif; font-size: 200%;">EXPLANATION  ||
 * 20x34x5=? || If we change the order to 20x5x34=? 20x5=100 & 100x34=3400!! EASY!! ||

<span style="color: #ff0057; font-family: Georgia,serif; font-size: 150%;">2.4 Questions?? <span style="color: #000080; font-family: 'Comic Sans MS',cursive; font-size: 120%;">Q.1 Find an easy way and calculate 4x16x50?? <span style="color: #000080; font-family: 'Comic Sans MS',cursive; font-size: 120%;">Q.2 I sell 50 lollypops at 90c each every day in October. How much did I earn?? <span style="color: #000080; font-family: 'Comic Sans MS',cursive; font-size: 120%;">Q.3 I have a 3 page essay, each line has 15 words on it and there are 38 lines per page. How many words have I written??

<span style="color: #ff0057; font-family: 'Arial Black',Gadget,sans-serif; font-size: 200%;">REVISION Questions??
<span style="color: #000080; font-family: 'Comic Sans MS',cursive; font-size: 120%;">Q.1 What are the factors of 72?? <span style="color: #000080; font-family: 'Comic Sans MS',cursive; font-size: 120%;">Q.2 What is the LCM of 4 and 32? <span style="color: #000080; font-family: 'Comic Sans MS',cursive; font-size: 120%;">Q.3 List the first 5 prime numbers?? <span style="color: #000080; font-family: 'Comic Sans MS',cursive; font-size: 120%;">Q.4 Is 12354 divisible by 5, 6, and 7?? <span style="color: #000080; font-family: 'Comic Sans MS',cursive; font-size: 120%;">Q.5 10x35x10=?? <span style="color: #000080; font-family: 'Comic Sans MS',cursive; font-size: 120%;">Q.6 Is 97 prime or composite??