prime factorization.. prime number composite numbers prime factorization factor tree
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Prime Factorization.
Prime number
Composite numbers
Prime factorization
Factor tree
Prime numbera number that has exactly two
factors 1 and itself.
7
13
29
2
Composite numberA 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.
300
3 100
10 10
2 52 53
×
×
× × × ×
×
The Prime Factorization
is 2×2×3×5×5
or 22 × 3 × 52
3
Find the prime factorization of 112.
112
2 56
7 8
2 472
×
×
× × ×
×
The Prime Factorization
is 2×2×2×2×7
or 24 × 7
2
2 272 × × × 2×
Find the prime factorization of 324.
324
2 162
2 81
9 922
×
×
× × ×
×
The Prime Factorization
is 2×2×3×3×3×3
or 22 × 34
2
3 322 × × × 3×3 ×
3001122×2×3×5×52×2×2×2×7
72
22
2
3
55
Make a Venn diagram from the prime factorization of 112 and 300.
The GCF is the product of the intersection numbers. (2 × 2 = 4)
The LCM is the product of ALL the numbers in the Venn diagram.
LCM: 2 × 2 × 2 × 2 × 3 × 5 × 5 × 7 = 8400
The LCM is the product of ALL the
numbers in the Venn diagram.
LCM: 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3 × 7 =
9072
The GCF is the product of the intersection numbers. (2 × 2 = 4)
324
112
2×2×3×3×3×3
2×2×2×2×7
72
22
2
3
33 3
Make a Venn
diagram from the
prime factorization
of 112 and 324.
The GCF is the product of the intersection numbers. (2 × 2 × 3 = 12)
The LCM is the
product of ALL the
numbers in the Venn diagram.
LCM: 2 × 2 × 3 × 3 × 3 × 3 ×
5 × 5 = 8100
324
3002×2×3×5×5
2×2×3×3×3×3
22
3
33 3
55
Make a Venn diagram from the prime factorization of 324 and 300.
324
3001122×2×3×5×5
2×2×3×3×3×3
2×2×2×2×7
72
22
2
3
33 3
55
7530
3×5×52×3×5
3
525
Make a Venn diagram from the prime factorization of 30 and 75.
The GCF is the product of the intersection numbers. (3 × 5 = 15)
2 15
2 3 5
×
× ×
3 25
3 5 5
×
× ×
The LCM is the product of ALL numbers. (2 × 3 × 5 × 5 = 150)
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