Sat math Essentials

b
and 
d
are incorrect. Answer choice 
a
is incorrect
because, although 
n
could equal 3, it does not necessarily equal 3. Answer choice 
c
is incorrect because
n
> 2.
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N U M B E R S A N D O P E R AT I O N S R E V I E W
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5 0

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P r i m e F a c t o r i z a t i o n
Prime factorization
is a process of breaking down factors into prime numbers.
Example
Let’s determine the prime factorization of 18.
Begin by writing 18 as the product of two factors:
18 
9 
2
Next break down those factors into smaller factors:
9 can be written as 3 
3, so 18 
9 
2 
3 
3 
2.
The numbers 3, 3, and 2 are all prime, so we have determined that the prime factorization of 18 is 3 
3 
2.
We could have also found the prime factorization of 18 by writing the product of 18 as 3 
6:
6 can be written as 3 
2, so 18 
6 
3 
3 
3 
2.
Thus, the prime factorization of 18 is 3 
3 
2.
Note:
Whatever the road one takes to the factorization of a number, the answer is always the same.
Practice Question
2 
2 
2 
5 is the prime factorization of which number?
a.
10
b.
11
c.
20
d.
40
e.
80
Answer
d.
There are two ways to answer this question. You could find the prime factorization of each answer
choice, or you could simply multiply the prime factors together. The second method is faster: 2
2
2
5 
4
2
5 
8
5 
40.