Prime Numbers

Prime Numbers

1. Prime Numbers

   • A prime number is a number that has exactly 2 different factors; itself and 1
   • 1 is not a prime number
   • Testing for prime numbers
     • 1. Find the square root of the number
       • 2. Check whether the number is divisible by prime numbers up to the square root
         • Eg. Is 307 a prime number?
           • The square root of 307 = 17.5
             • If 307 is not divisible by 2,3,5,7,11,13,17, then it is a prime number

2. Multiples

   • Numbers in the times table
     • Eg. Multiples of 7 are 7,14,21,28,35,42...

3. Factors

   • The numbers that divide into a number
     • Eg. the factors of 12 are 1,2,3,4,6,12 as 12 is divisible by all these numbers
       • The easiest ways to find the factors of a number is to list them in pairs
         • Eg. factors of 36: 1 and 36, 2 and 18...

4. Products of prime numbers

   • To find the product of prime factors of a number it is useful to draw a factor tree
     • 36
       • 4
         • 2
         • 2
       • 9
         • 3
         • 3
           • 2 x 2 x 3 x 3
             • This is the product of the prime factors of 36

5. Highest common factor and Lowest common multiple

   • Use a factor tree for all numbers
     • Make a venn diagram. Label that circles with each number. Put the common prime factors in the section where both circles cross.
       • To find the highest common factor multiply the numbers in the section where both circles cross.
       • To find the lowest common multiple multiply all the numbers in the venn diagram