Factoring

Factoring

1. GREATEST COMMON FACTOR

   • To find the GCF of two number we must first figure out the factors of each of the number.
     • Example: GCF(12, 8) 12: 1, 2, 3, 4, 6, 12 8: 1, 2, 4, 8
       • Write out all the factors of 12 & 8
       • We have now figured out all of the factors of 12 & 8
       • Now we need to find the greatest factor they have in common and that would be 4.
       • So the GCF(12, 8) = 4
     • If the number is a prime number it only has two factors 1 and itself.
       • When two numbers have a GCF of only 1 they are called relatively prime.

2. FACTORS AND FACTORIZATION

   • You can find a numbers prime factorization using a factor tree. This means that by usign a factor tree you will not find all the factors of a number but you will find its prime factor.
     • For example, this factor tree shows the prime factors of 108. It also shows some of it other factors like 54 and 18. However, this factor tree does not show every factor of 108.
   • A good way to find all the factors of a number is to keep a factors list.
     • For example, when we look for the factors of 120 we can keep a list to the side of all the factors we have found.
       • 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
         • 120= 2*60 120= 3*40 120= 4*30 120= 5*24 120= 6*20 and so on........
         • Doing it this way allows you to find ALL the factors of a number not just the prime ones.

3. DIVISIBILITY AND FACTORS

4. When you are trying to find out if a number is divisible by 2 the only thing you do is look at the digit of a number in the ones place. When you look at that see if that number is divisible by 2.

   • Example: 2, 799, 588 8 is divisible by 2 because 4*2=8 so therefore, this number is divisible by 2.
   • If you wanted to figure out if a the number was divisible by 3 then you will need to add up all of its numbers and see if the sum is divisible by 3. The same applies when trying to find out if a number is divisible by 9.
     • Example: 2, 799, 588 2+7+9+9+5+8+8= 48 and 48 is divisible by three because 3*16=48 However, if you were still not sure if 48 was divisible by 3 you could add the 4 and 8 together. You would do 4+8=12 and 12 is divisible by 3.
     • If you want to learn if a number is divisible by 4 then you will look at the last two digits and see if they are divisible by 4.
       • If your last digit is a 0 or 5 then the number is divisible by 5.
         • If a number is divisible by 2 and 3 then it is also divisible by 6. This is because the prime factorizatuion of 6 is 3*2.
           • If a number has a zero in the ones place then the number is divisible by 10.

Imágenes y archivos del mapa