Download Prime Factorization Factor Trees

Prime Factorization
Factor Trees
ACTIVITY
1.3
SUGGESTED LEARNING STRATEGIES: Think/Pair/Share
My Notes
The prime factorization of a number shows the number as a
product of factors that are all prime numbers. One way to find the
prime factorization of a number is to use a factor tree.
• Use divisibility rules to find two factors of the number.
• Check whether the factors are prime or composite.
• If both are prime, stop. If not, continue factoring until all factors
are prime numbers.
EXAMPLE 1
Find the prime factorization of 12.
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Step 1:
Write 12.
12
Start with two factors of 12.
Try 3 and 4.
3×4
Use branches to show the factors.
Step 2: Check: 3 is a prime number, but
12
4 is not.
Continue by factoring 4.
3×4
Don’t forget to rewrite the 3
3×2×2
with the factors of 4.
Solution: Check again. All factors are now prime numbers, so this is
the prime factorization of 12.
TRY THESE
Find the prime factorization of:
a. 15
b. 16
1. Will the prime factorization of 12 be different if you start with
the factors 2 and 6? Draw another factor
tree starting with 2 and 6.
MATH TERMS
The Fundamental Theorem of
Arithmetic states that any whole
number greater than 1 can be
written as a product of prime
factors in only one way. The
order of the factors may vary.
Unit 1 • Number Concepts
15
ACTIVITY 1.3
Prime Factorization
continued
Factor Trees
SUGGESTED LEARNING STRATEGIES: Create
Representations
My Notes
ACADEMIC VOCABULARY
The prime factorization of a
number can be written using
exponents. An exponent tells how
many times the base number is
used as a factor.
34
Prime factorization can be written two ways:
• as the product of prime factors: 2 × 2 × 3
• using exponents: 22 × 3
2. Use factor trees to write the prime factorizations of 25 and 36.
Exponent
Base
34 = 3 × 3 × 3 × 3
3. Write each number using exponents.
a. 2 × 2 × 2 × 3 × 3
b. 3 × 3 × 5 × 7 × 7
c. 2 × 3 × 3 × 13 × 13 × 13
4. Write the following numbers as products of prime factors.
b. 32 × 53
CHECK YOUR UNDERSTANDING
Write your answers on notebook paper.
Show your work.
4. Write 48 as a product of prime factors and
then using exponents.
1. Write the prime factorization of 100.
5. Is 2 × 3 × 4 the prime factorization of 24?
Explain your reasoning.
2. Write the prime factorization of 72 using
exponents.
3. Write 32 × 43 as a product of prime factors.
16
SpringBoard® Mathematics with Meaning™ Level 1
6. MATHEMATICAL How are 4 × 2 and 42
R E F L E C T I O N different? Explain your
thinking.
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a. 24