Download Lesson 2: Factors and Prime Factorization

Unit 2: Understanding Positive Real Numbers
Lesson 3: Factors and Prime Factorization
Vocabulary:
1. factor – whole numbers that are multiplied to find a product (Ex. The “factors” of 12 are 1, 2, 3, 4, 6, and 12.)
2. prime factorization – a number written as the product of its prime factors (Ex. The “prime factorization” of 12 is 2 x 2 x 3.)
3. divisible- when a number is able to be evenly divided by another number with a remainder of zero.
4. composite number- numbers that are divisible by more than two numbers.
5. prime number- a number that is divisible by only the numbers 1 and itself.
A number is divisible by…
2 if the last digit is even
3 if the sum of the digits is divisible by 3
4 if the last two digits form a number
divisible by 4
5 if the last digit is 0 or 5
6 if the number is divisible by both 2 and 3
9 if the sum of the digits is divisible by 9
10 if the last digit is 0
Divisibility Rules
Divisible
3,978
315 (3 + 1 + 5 = 9)
8,512
Not Divisible
4,975
139 (1 + 3 + 9 = 13)
7,518
14,975
48
711 (7 + 1 + 1 = 9)
15,990
Checking Divisibility
10,978
20
93 (9 + 3 = 12)
10,536
TRY THESE:
Tell whether 610 is divisible by 2, 3, 4, and 5. ______________________
Tell whether 387 is divisible by 6, 9, and 10. _______________________
Identifying Prime and Composite Numbers
Tell whether each number is prime or composite.
A. 45
B. 13
C. 19
D. 49
Finding Factors
*We are Factor Ninjas! We have come to FLMS to chop numbers into smaller numbers (their factors)! *
*Helpful Hint: When finding factors, use your math facts! Start with one and the number itself. Then build up from one (2, 3, 4…).
Once you get to a math fact that repeats factors you’ve already used, you are done.
Example 1A:
List all of the factors of:
Example 1B:
List all of the factors of:
18
1 * 18
2*9
3*6
*4 and 5 are not factors of 18, and 6 would repeat, so you are
done!*
Now, in a U direction, list the numbers. The factors will be
written in order from least to greatest! 
24
1 * 24
2 * 12
3*8
4*6
*5 is not a factor of 24, and 6 would repeat, so you are done!*
Now, in a U direction, list the numbers. The factors will be
written in order from least to greatest! 
TRY THESE:
List the factors of the following number:
1.
12: ______________________________________________________________
2.
21: ______________________________________________________________
3.
52: ______________________________________________________________
4.
75: ______________________________________________________________
Writing Prime Factorization
Method: Ladder Diagram
*This method involves dividing your number by prime factors.
Step 1: Divide 30 by a prime number.
Step 2: Divide that quotient by another prime number.
Step 3: Keep dividing until you get 1 for a quotient.
Step 4: The prime numbers on the outside of the ladder are all the prime factors of that number. Using those
prime factors, write a multiplication problem with the numbers written from least to greatest.
*Remember: all factors in prime factorization MUST be PRIME!*
TRY THESE: Use the ladder method to find the prime factorization of the following numbers:
1.)
14
2.)
18
3.)
63
4.)
54