Transcript Number Theory, Part 3

Factorization
• Factorization is writing a number as a
product of factors.
24
60
Prime Factorization
• A factorization of the number in which all
of the factors are prime numbers.
10
12
Prime Factorization
• 24
• 25
Prime Factorization
Using a factor tree to do prime factorization.
60
Find the prime factorization
112
Prime Factorization
Using factor tree or division method
24
24
Using prime factorization
to get all factors
24  2  3
3
Use the prime factorization to get all the the
factors of 24.
Factor vs Multiple
24
Factors
Multiples
Common Factors
12
18
Greatest Common Factor
Also known as GCF
12
18
GCF
• You try
24
30
Common Multiples
6
10
Least Common Multiple or LCM
12
18
22 . 3
2 ∙ 32
Let’s try a few more
•
•
•
•
The LCM of 28 and 140
126 = 2 • 3 • 3 • 7
140 = 2 • 2 • 5 • 7
Think: both 140 and 126 are factors of the LCM.
Start with either factor:
• 126 (factors: a 2, two 3s, and a 7). From 140,
we still need a 2 and a 5.
• LCM = 126 • 2 • 5 = 1260.
• Check: 1260 = 140 • 3 • 3 = 1260
Word Problem Example
Tara can run around the track in 5 minutes. Todd
can run the same distance in 6 minutes, and
Tony can do it in 8 minutes. If they start at the
same time, when will they next meet at the
starting line?
Find the LCM of 5, 6, and 8