Transcript 2 - Granicher

#1
RULES FOR DIVISIBILITY
IF
A Number Is
Divisible By:
2
3
4
5
6
8
9
10
The last digit is even (0, 2, 4, 6, 8)
The sum of the digits is divisible by 3
The last 2 digits are divisible by 4 (÷2÷2)
The last digit is 0 or 5
It is divisible by 2 and 3
The last 3 digits are divisible by 8 (÷2÷2÷2)
The sum of the digits is divisible by 9
The last digit is 0
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#2
IS THE NUMBER DIVISIBLE EXACTLY BY?
WRITE yes (y) or no (n) REMEMBER: Show the
sums for 3, and show the division for 4 and 8.
Number
2
3
1)
360
y
3+6 = 9
y
4
30
2) 60
15
2) 30
y
5
y
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6
y
8
180
2)360
90
2)180
45
2) 90
y
9
y
10
y
#3
FACTOR
A Factor is a number that is multiplied
by another number to give the product.
7 x 8 = 56
Factors
A Factor is the number that divides evenly
into another number.
56 ÷ 8 = 7
Factor
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#4
Prime & Composite
Prime NumbersA Prime number is a whole number
with exactly 2 factors, one and itself.
Example: 17, 3, 2, 11, 13, 5
Composite NumbersA Composite number is a number that
has more than two factors.
Example: 9, 30, 64, 8, 40, 69
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#5
Prime Factorization is when you write a
number as the product of prime numbers.
36
Circle the
prime
numbers
2
 Factor Tree
18
2 9
3
3
36  2  2  3  3
2
2
36  2  3
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#6
Make A List
Making a list can be helpful to keep track of
data and to spot any missing data.
To make a list start with the lowest possible
factor which is 1.
Factors of 36
1 x 36
2 x 18
3 x 12
4x9
6x6
We know we
didn’t miss any
Factors because
our list is
ORGANIZED!
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Factors of 24
1 x 24
2 x 12
3x8
4x6
#7
GCF, Make a List Method #1
GCF is the largest number that is a factor of 2 numbers.
It is useful to know this for reducing fractions.
Step 1: List all the factors of both numbers.
Step 2: Then find the greatest common factor.
Ex.
Factors of 12
1 x 12
2x 6
3x 4
Factors of 30
1 x 30
2 x 15
3 x 10
5x 6
Common Factors are 1,2,3,6 GCF= 6
This method is only useful if both numbers are small
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#8
Find the prime factorization of the 2 numbers.
Step 2: Then multiply their common factors.
Step 1:
30
12
2
2 15
6
2
3
3
2 23
5
2  3 5
Factors the 2 numbers have in common are: 2 & 3
Multiply the common factors. GCF  2  3  6
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#9
Multiples
A number that is added to itself
becomes a multiple.
Multiples of 3 = 3, 6, 9, 12, 15, 18 .
..
Multiples can go on infinitely forever.
The least common multiple (LCM) is the
least common number that is a multiple of 2
numbers.
It is useful to know this for adding fractions.
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#10
LCM Make a List Method # 1
TO FIND THE LCM OF 4 and 12:
1) List the multiples of both numbers
4 = 4, 8, 12, 16, 20…
12 = 12, 24, 36…
2) Find the least multiple that
both numbers have in common.
LCM is 12
This method is useful if both numbers are small.
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#11 LCM Prime Factorization Method # 2
1) List
the prime factorization to find the LCM.
20
18
2
2 10
9
3
3
2
2  3 3
2)
3)
5
2 25
Select all common factors once.
Select all remaining factors, and multiply.
LCM  180
LCM  2 332 5
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