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Transcript 
Prime
Factorization.
Prime number
Composite numbers
Prime factorization
Factor tree
Prime number
a number that has exactly two
factors 1 and itself.
7
13
29
2
Composite number
A number that is not prime
A number that has more than
two factors
4 (1, 2, 4)
24 (1, 2, 3, 4, 6, 8, 12, 24)
18 (1, 2, 3, 6, 9, 18)
Prime factorization
writing a number as a product
of prime numbers.
Find the prime
factorization of 300.
The Prime
Factorization
is
2×2×3×5×5
or
2
2
2 ×3×5
300
3 × 100
3 × 10 × 10
3 × 2 × 5 × 2× 5
Find the prime
factorization of 112.
The Prime
Factorization
is
2×2×2×2×7
or
4
2 ×7
112
2 × 56
2 × 7 × 8
2 × 7 ×2 × 4
2 × 7 ×2 × 2 × 2
Find the prime
factorization of 324.
The Prime
Factorization
is
324
2 × 162
2×2×3×3×3×3 2 × 2 × 81
or
2
4
2× 2 × 9× 9
2 ×3
2 × 2 × 3× 3× 3× 3
Make a Venn diagram from the prime
factorization of 112 and 300.
TheThe
GCF
is the
of the
intersection
LCM
is product
theLCM:
product
of ALL
the
(2Venn
=×4)7 = 8400
2 ×numbers
2 × numbers.
2 × 2in×the
3×
5××25diagram.
2
7
2
112
2×2×2×2×7
3
2
2
5
5
300
2×2×3×5×5
324
The GCF is the
product of the
intersection
numbers.
(2 × 2 = 4)
3
2
7
2
112
2×2×2×2×7
3
Make a Venn
2×2×3×3×3×3
diagram
from the
3
prime
factorization
of 112 and
3
324.
2
2
The LCM:
LCM is the
product of ALL the
2×2×2×2×3
numbers in the Venn
× 3 ×diagram.
3×3×7=
9072
Make a Venn
diagram from
the prime
factorization
of 324 and
300.
324
3
3
3
3
2
The GCF is the
product of the
intersection
numbers.
(2 × 2 × 3 = 12)
2×2×3×3×3×3
2
5
TheLCM:
LCM
2×2×
is 3the
×
3product
× 3 × 3 of
×
ALL
5 × 5the
=
numbers
8100
in
the Venn
5 diagram.
300
2×2×3×5×5
324
3
2
112
2×2×2×2×7
3
3
3
2
7
2×2×3×3×3×3
2
2
5
5
300
2×2×3×5×5
Make a Venn diagram from the prime
factorization of 30 and 75.
The GCF
intersection
LCMisisthe
theproduct
productof
ofthe
ALL
numbers.
numbers.
15)
(2 × 3 × 5(3× ×5 5= =150)
30
2
75
3
× 15
2 ×3 × 5
2×3×5
2
5
5
3
× 25
3 ×5 × 5
3×5×5
What does it mean if the Venn
diagram of the prime
factorizations of two numbers
had no numbers in the
intersection?
Find two numbers that would
have a Venn diagram like this.
Find the prime
factorization of -630.
Homework
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