Transcript Write the prime factorization of the number.

Prime Factorization
A prime number is a whole number greater than 1
that has exactly two factors, 1 and itself.
Three is a prime number because its only factors are
1 and 3. What are the rest of the prime numbers?
A composite number is a whole number that
has more than two factors.
Six is a composite number because it has more
than two factors—1, 2, 3, and 6. The number 1
has exactly one factor and is neither prime nor
composite.
Tell whether each number is
prime or composite.
A. 11
The factors of 11
are 1 and 11.
11 is prime.
B. 16
The factors of 16 are
1, 2, 4, 8, and 16.
16 is composite.
Tell whether each number is
prime or composite.
C. 14
D. 7
The factors of 14
are 1, 2, 7, and 14.
The factors of 7
are 1 and 7.
14 is composite.
7 is prime.
A composite number can be written as the
product of its prime factors. This is called
the prime factorization of the number.
You can use a factor tree to find the prime
factors of a composite number.
Writing Math
You can write prime factorization by using
exponents. The exponent tells how many times
to use the base as a factor.
Write the prime factorization of
each number.
24
8 ·3
4 · 2
2 ·2
Write 24 as the product of
two factors.
Continue factoring until all
factors are prime.
The prime factorization of 24 is
2 · 2 · 2 · 3 or 23 · 3.
Write the prime factorization of
each number.
150
30 · 5
10 · 3
Write 150 as the product
of two factors.
Continue factoring until
all factors are prime.
2·5
The prime factorization of 150
is 2 · 3 · 5 · 5, or 2 · 3 · 52.
Write the prime factorization of
each number.
36
18 · 2
9·2
Write 36 as the product of
two factors.
Continue factoring until all
factors are prime.
3·3
The prime factorization of 36 is
2 · 2 · 3 · 3 or 22 · 32.
Write the prime factorization of
the number.
90
45 · 2
9·5
Write 90 as the product
of two factors.
Continue factoring until
all factors are prime.
3·3
The prime factorization of 90
is 3 · 3 · 5 · 2, or 2 · 32 · 5.
ASSIGNMENT
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You can also use a step diagram to find
the prime factorization of a number. At
each step, divide by the smallest
possible prime number. Continue
dividing until the quotient is 1.
Repeated Division
Start by dividing
by the smallest
prime number.
Keep using 2
until it will not
work anymore.
2 40
2 20
2 10
5 5
1
When you get to 1
you are finished
2 x 2 x 2 x 5 = 2³ x 5
Let’s try another one…
Start by dividing
by the smallest
prime number.
2 will no longer
work so you
need to try the
next prime
number…3!
2 42
3 21
7 7
1
2x3x7
When you
get to 1
you are
finished
Now you try!
2 18
3 9
3 3
1
2 x 32
2
2
7
28
14
7
1
22 x 7
Write the prime factorization of the number.
325
5 325
5 65
13 13
1
Divide 325 by 5. Write the quotient
below 325.
Stop when the quotient is 1.
The prime factorization of 325 is 5 · 5 · 13, or
52 · 13.
Write the prime factorization of the number.
275
5 275
5 55
11 11
1
Divide 275 by 5. Write the quotient
below 275.
Stop when the quotient is 1.
The prime factorization of 275 is 5 · 5 · 11, or
52 · 11.
Write the prime factorization of each number.
476
2 476
2 238
7 119
17 17
1
Divide 476 by 2. Write the
quotient below 476.
Keep dividing by a prime
number.
Stop when the quotient is 1.
The prime factorization of 476 is 2 · 2 · 7 · 17, or
22 · 7 · 17.
There is only one prime factorization for any
given composite number. The last example
began by dividing 476 by 2, the smallest prime
factor of 476. Beginning with any prime factor
of 476 gives the same result.
2 476
2 238
7 119
17 17
1
7 476
2 68
2 34
17 17
1
The prime factorizations are 2 · 2 · 7 · 17 and
7 · 2 · 2 · 17, which are the same as 17 · 2 · 2 · 7.