Transcript Dividing by 2 - Sage Middle School

Greatest Common Factor
Definition: The Greatest Common Factor is the largest
number that will divide into two other numbers or the
number that contains all the factors common to both
numbers.
Example: the Greatest Common Factor of 2940 and
3150 is found by finding all the prime numbers they
have in common and multiplying them.
2940: 2 x 2 x 3 x 5x7x7
3150:2x3x3x5x5x7
You can see that the numbers in red are what they have
in common therefore the Greatest Common Factor is
2x3x5x7 =210
Least Common Multiple
• Definition: The Least Common Multiple is the smallest
number that two numbers will divide into. In other words
all of the factors of the two numbers have to be used.
• An example of the Least Common Multiple of 2940 and
3150 are as follows.
• 2940: 2 x 2 x 3 x 5x7x7
• 3150:2x3x3x5x5x7
• Therefore the LCM is found by multiplying
• 2x2x3x3x5xrx7x7 = 44100
• Caution do not overuse a factor. Don’t count both top and
bottom just the maximum times it appears in either the top
or bottom.
Factor
• To factor a number means to break it up into
numbers that can be multiplied together to
get the original number.
• Example 14 = 7x2 so 7 and 2 are factors of 14.
Prime Number
• A prime number is a natural number greater
than 1 that has no positive divisors other than
one or itself.
• Examples include 7 and 13.
Composite Numbers
• Composite Numbers are numbers are Natural
Numbers greater than one and not prime.
• Examples include 2, and 9.
Natural Numbers
• Natural numbers: There is some debate as to
whether natural numbers include zero or not,
but basically they are the positive numbers
and do not include fractions.
Practice
Find the LCM and GCF for each set of
numbers
1) 105
310
2)306
204
3) 123
321
4) 125
275
Divisibility Rules
Dividing by 2
All even numbers are divisible by 2. E.g., all numbers ending
in 0,2,4,6 or 8.
Dividing by 3
Add up all the digits in the number.
Find out what the sum is. If the sum is divisible by 3, so is the
number
For example: 12123 (1+2+1+2+3=9) 9 is divisible by 3,
therefore 12123 is too!
Dividing by 4
Are the last two digits in your number divisible by 4?
If so, the number is too!
For example: 358912 ends in 12 which is divisible by 4, thus
so is 358912.
Divisibility Rules
• Dividing by 5
• Numbers ending in a 5 or a 0 are always
divisible by 5.
• Dividing by 6
• If the Number is divisible by 2 and 3 it is
divisible by 6 also.
Distributive Property
The Distributive Property of multiplication
is the property that states that multiplying
a sum by a number is the same as
multiplying each addend by the number
and then adding the products. The
Distributive Property says that if a, b and c
are real numbers,
then a(b + c) = (a x b) + (a x c)
Examples of Distributive property
36 + 8 = 44
Step 1
Step 2
Answer
4 (9 + 2) =
(4 x 9) + (4 x 2) =
36
+
8 = 44
Practice
1) 2 (x + 3)
2) 4 ( 6 + 5)
Are these equal?
3) 40 + 9 =
4) 63 + 3 =
7 (7 + 0) =
11 (6
+ 1) =