Download Number Sense Continued… (Part 4)

Number Sense
Continued… (Part 4)
Prime Factorization, GCF, & LCM
Prime Factorization
The breaking down of a composite number as the product of
its prime factors.
Example:
24
 2
12
2
6
2
3
Prime Factorization: 2 × 2 × 2 × 3 or 23 × 3
 The prime numbers are written in order from least to
greatest.
 Practice
a) 260
b) 1800
c) 3600
Answers
a) 260
b) 1800
26
18
10
2 13 2 5
2 9
100
4 25
3 3 22 5 5
PF: 2×2×5×13
22 ×5×13
c) 3600
PF:2×2×2×3×3×5×5
23 ×32 ×52
36
6
100
6
4 25
23 23 2255
PF:2×2×2×2×3×3×5×5
24 ×32 ×52
GCF
 “GCF”
stands for “Greatest Common Factor”
 There are two methods of finding the GCF:
 First
Method: Given two numbers, (20 & 30), list all the
factors of each given number.
20: {1, 2, 4, 5, 10, 20 }
30: {1, 2, 3, 5, 6, 10, 15, 30 }
GCF = 10
 The largest factor they both share is the GCF.
GCF
 Second
Method: Given two numbers, (20 & 30), break
them down to their prime factorization.
20
2
10
P.F: 2 × 2 × 5
30
2
P.F: 2 × 3 × 5
15
2
5
3 5
Multiply the factors they share; the product is the GCF.
GCF = 10
Practice
 Find
the GCF of 90 and 50, using Prime Factorization.
Answer
 Find
the GCF of the following numbers: 90 & 50
90
50
9
10
3 3
2
P.F: 2 × 3 × 3 × 5
The GCF is 10
5
5
10
2
P.F: 2 × 5 × 5
5
Practice
 Find
the Prime Factorization of 100 and 225 listing all the
factors:
Answer
 Find
the Prime Factorization of 100 and 225 listing all the
factors:
100: {1, 2, 4, 5, 10, 20, 25, 50, 100}
225: {1, 3, 5, 9, 15, 25, 45, 75, 225}
 The
GCF is 25.
Review: Find the LCM of each pair of
numbers.
 1)
8, 12
 2)
9, 21
 3)
12, 15
 4)
18, 24
Review: Find the LCM of each pair of
numbers.
 1)
8, 12
8: 8, 16, 24, 32, 40, 48, 56,….
12: 12, 24, 36, 48, 60, 72,….
LCM = 24
 2)
9, 21
9: 9, 18, 27, 36, 45, 54, 63, 72, 81,…
21: 21, 42, 63, 84, 105, 126, 147,…
LCM = 63
Review: Find the LCM of each pair of
numbers.
 3)
12, 15
12: 12, 24, 36, 48 60, 72,84,…
15: 15, 30, 45, 60, 75, 90, 105,…
LCM = 60
 4)
18, 24
18: 18, 36, 54, 72, 90, 108, 126,…
24: 24, 48, 72, 96, 120, 144, 168,…
LCM = 72
Video
 Source:
“LCM and GCF (greatest common factor)” Khan
Academy,Youtube, 24 July 2013. Web. 26 August 2013.