# Download Prime Time Notes Factors Factors: a number that can be multiplied

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```Prime Time Notes
Factors
Factors: a number that can be multiplied to get another number
Example: 5 is a factor of 30
Factor pairs: two numbers that can be multiplied together to get another number
Example: 5 and 6 is a factor pair of 30
Finding Factors: use the division test and test every number to write down factor pairs until you
reach a number that is already written as a factor.
Example: Find the factors of 30
,30
Then try other numbers using divisibility rules to help
1, 2, 3, 5, 6, 10, 15, 30
Prime number: a number with exactly 2 factors, one and the number itself
Composite number: a number with more than 2 factors
Multiples
Multiples: a number that can be gotten by multiplying the original number
Example: 30 is a multiple of 5
Finding multiples: multiply the number by 1, 2, 3, etc. continuing until you have the desired
number of multiples.
Greatest Common Factor: the biggest factor shared by two numbers
Example: Find the GCF of 12 and 30
12: 1, 2, 3, 4, 6, 12
30: 1, 2, 3, 5, 6, 10, 15, 30
Since 6 is the largest number on both lists, 6 is the GCF.
Least Common Multiple: the smallest multiple shared by two numbers
[note: If the numbers are relatively prime (do not share any factors but 1) their LCM will be the
product of the number. Ie. The LCM of 5 and 11 is 5x11=55.)
Example: Find the LCM of 4 and 6
4: 4, 8, 12, 16, 20,…
6: 6, 12, 18, 24, …
Since 12 is the smallest number on both lists, 12 is the LCM.
Square numbers: any number multiplied by itself makes a square number
Example: 16 is a square number because 4 x 4 = 16
List of square numbers from 1 to 100: 1, 4, 9, 14, 25, 36, 47, 64, 81, 100
Order of Operations
1. Parentheses
2. Exponents
3. Multiplication and Division from left to right
4. Addition and Subtraction from left to right
Example:
12 ÷ 2 x 3 – 4 + 23 + (2+3x1)
12÷ 2 x 3 – 4 + 23 + (2 +3)
12 ÷ 2 x 3 – 4 + 23 + 5
12 ÷ 2 x 3 – 4 + 8 + 5
6x3–4+8+5
18 – 4 +8 + 5
14 + 8 + 5
22 + 5
27
Prime Factorization: A number written as a product of prime numbers.
A factor tree is a good way to find prime factorization.
The prime factorization of 100 =2 x 2 x 5 x 5 (expanded form)
And 100 = 22 x 52 (exponential form)
```