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Prime, Composite,
and
PRIME FACRTORIZATION
Prime numbers have EXACTLY 2 factors...1 and themselves
Composite numbers have 3 OR MORE factors.
The number 1 is not prime or composite because it only
has 1 factor. 1 is the multiplicative identity, which just
means anything multiplied by 1 is itself.
All composite numbers can be broken down to a product of
prime factors.
Start with the lowest prime number that the number is
divisible by and stick with it as long as you can. Go up to the
next factor and repeat until ALL FACTORS are PRIME.
2,3,5,7,11,13 are the first six primes.....
Prime Factors for 210
210
2
105
3
35
5
7
Prime Factors of 210 are 2 x 3 x 5 x 7
Exponents
BASEExponent
Exponents are the little numbers written up and to the right
in a mathematical problem.
The exponent tells you how many times to use the base as a
factor.
Exponents are the second step in order of operations.
The E in PEMDAS
42 means 4 x 4 or 16
35 means 3 x 3 x 3 x 3 x 3 or 243
DO NOT MULTIPLY THE BASE BY THE EXPONENT
FACTORS
Factors are the numbers you multiply to get a
product. The factors of a number start with 1 and end
with that number. T-charts are a good way to list
factors.
factor x factor = product
Factors of 48
1
2
3
4
6
48
24
16
12
8
Factors of 30
1
2
3
5
30
15
10
6
Because these are all possible factor pairs of 48 and
all the possible factor pairs of 30.
The GCF (Greatest Common Factor) of 48 and 30 is 6
because 6 is the largest number that appears on both
lists.
MULTIPLES
Multiples of a number are what you get when you
multiply a number by 1,2,3,4,5,6,....
You could continue listing multiples of a number
forever and the list would never end.
Multiples of 5
5,10,15,20,25,30,35,40,45.....
Multiples of 9
9,18,27,36,45,54,63,72,81...
The LCM (least common multiple) of 5 and 9 is 45
because 45 is the first multiple that appears on both
lists.
The two numbers multiplied together is always a
common multiple but sometimes there is one before
that. LCM of two numbers will NEVER be greater than
the 2 numbers multiplied by each other.
Mulitples of 4
4,8,12,16,20,24
Multiples of 6
6,12,18, 24
The LCM of 4 and 6 is 12.