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Transcript
```4-2
Prime Factorization
Objective
• To use divisibility rules to check for divisibility
and write the prime factorization of numbers
in exponential form.
• Why? To help you with prime factoring,
simplifying fractions, division.
California State Standards
NS 1.4
(Gr. 5): Determine the prime factors of
all numbers through 50 and write the numbers
as the product of their prime factors by using
exponents to show the multiples (e.g., 24 = 2 x 2
x 2 x 3 = 2³ x 3)
MR 3.3: Develop generalizations of the results
obtained and the strategies used and apply
them in new problem situations.
Vocabulary
• Divisible
– A number is divisible by another number if the remainder is
zero after dividing.
• 36 ÷ 6 = 6
• Prime Number
– A whole number greater than one with only two factorsitself and one.
• 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 57, 59, …
• Composite Number
– A whole number greater than one that has more than two
factors
• 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, …
• Prime Factorization
– Writing a number as the product of its prime factors
• 24 = 2 x 2 x 2 x 3
Divisibility Rules!
Divisibility Rules
A number is divisible by:
2
If the last digit ends in 0, 2, 4, 6, 8 (any even number)
3
If the sums of the digits is divisible by 3 (may be even or odd)
4
If the last two digits are divisible by 4 (only an even number)
5
If the last digit ends in 0 or 5 (any number ending in 5 or 0)
6
If the number is divisible by 2 and 3 (only an even number)
9
If the sum of the digits is divisible by 9 (may be even or odd)
10
If the last digit ends with a 0 (only ends in 0)
How To Prime Factor - #1
• Make a ‘Factor Tree’
40
2 x 20
5x4
2x2
= 2³ x 5
Factor out each number until you get only primes
Circle the prime numbers to be organized
Put final answer in exponential form
How to Prime Factor- #2
Make a ‘Factor Ladder’
Put the number at the top of a
If it is even, begin ÷ 2
If not, try greater primes like 3,
5, 7, 9
Only move on when the current
number you are using doesn’t
work anymore
Use the divisibility rules to help
The numbers on the side of the
ladder are the numbers used
for prime factorization.
prime factor 40
40
2
20
2
10
2
5
= 2³ x 5
Try It!
Tell if each number is divisible by:
2, 3, 4, 5, 6, 9,or 10
1) 3,742
2) 5,310
3) 47,388
4) 9,999
5) 41, 112
1) 2
2) 2, 3, 5, 6, 9, 10
3) 2, 3, 4, 6
4) 3, 9
5) 2, 3, 4, 6, 9
Try Some More!
1)
64
Use exponents to
write the prime
factorization of
each number.
1) 64
2) 48
3) 76
2
32
2
16
2
8
2
4
2
2
64 = 2⁶
2)
3)
76
2
38
2
19
76 = 2² x 19
48
2
24
2
12
2
6
2
3
48 = 2⁴ x 3
More to Try
Prime factor using exponents.
9)
9) 81
81
9
9
3x3
3x3
81 = 3⁴
10) 90
10)
90
9
10
3x3
5x2
90 = 2 x 3² x 5
Objective Review
• To use divisibility rules
to check for divisibility
and write the prime
factorization of
numbers in exponential
form.
• Why? You can now
prime factor efficiently,
simplify fractions, and
divide better
Independent Practice
• Complete problems 1223
• Copy original problem
first.
• Show all work!
• If time, complete Mixed
Review: 24-29
• If still more time, work
on Accelerated Math.
```