Name:______________________________________
Ch 2 Prime Factorization 6th Gr
____
Date:________________
1. Define relatively prime. ___A pair of numbers that only share 1 as a common factor._____________
Write yes beside each pair of relatively prime numbers, and no beside each pair of numbers that are not
relatively prime:
a.
b.
c.
d.
____
9 and 12 _no______
24 and 36 __no_____
18 and 25 ____yes___
123 and 456 ___no___(The divisibility rule for 3 works for this.)
2. What is the least common multiple of 18, and 24? (Show or write the method you used to determine the LCM.)
LCM: 6
____
3. Is a common multiple always the least common multiple? Why or why not? _____No. Because you can
multiply two numbers to get a common multiple, but if they share common factors, they will share a smaller
common multiple.
________________________________________________________________________________________
Which of the following are multiples of 9 and 4? Write yes or no.
a. 9 ___no___
b. 36 __yes____
c. 56 __no_____
d. 72 ____yes___
____
4. Lisa and Laurie are making popcorn balls and brownies for the Fall Festival. It takes Lisa 15 minutes to roll a
batch of popcorn balls, and it takes Laurie 25 minutes to complete a batch of brownies. If Lisa and Laurie
complete a batch of popcorn balls and brownies at the same time, after how many minutes will they complete
another batch of popcorn balls and brownies at the same time? Either show or explain how you determined your
solution. ______In 75 minutes they will both have completed a batch of popcorn balls and
brownies._______________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
____
5. Restate the following theorems or properties in your own words:
a. Fundamental Theorem of Arithmetic: _All natural numbers except for one can be expressed as either a
prime number or the product of prime
numbers._____________________________________________________________________________
___________________________________________________________________________________
b. The Commutative Property of Multiplication: __The factors of a multiplication problem can be rearranged
and it will result in the same
product._______________________________________________________________
c. The Associative Property of Multiplication: ___The factors in a multiplication problem can be grouped in
different ways, and the product will remain the same.
_____________________________________________________________________________________
___________________________________________________________________________
d.
a
____
6. What is the greatest common factor of 36 and 108? Show your work or explain your thinking. __GCF= 36
because 36 x 3 = 108.___________
____
7. Label the parts of this number written in exponential notation.
base
64
exponent
power
____
8. The prime factorization of one number is 23 x 33. The prime factorization of another number is 32 x 5. What is
the prime factorization of the least common multiple of these two numbers? 23 x 33 x 5
____
9. What is the prime factorization of 72? Either show your work or explain your thinking.
2 x 2 x 2 x 3 x 3 = 23 x 32
____ 10. What is the relationship between 18 and 36 in terms of factors and multiples?
Is 18 a multiple of 36? no
Is 18 a factor of 36? yes
Is 36 a multiple of 18? yes
Is 36 a factor of 18? no
____ 11. What is the value of 63? Show your work or explain your thinking. 216 because that is the product of 6 x 6 x 6.
____ 12. Richard is distributing snack bags to friends. He must give the same number of snack bags to each friend and
use all the snacks. He has 12 cookies and 18 bags of trail mix. What is the greatest number of friends he can give
snack bags to? Show your work or explain your thinking. 6 friends can each get the same items in a snack bag.
____ 13. How do you express 2 x 3 x 3 x 5 x 5 x 5 with powers? 2 x 32 x 53
____ 14. Kayla is buying pom-poms and stickers to hand out at the football jamboree. Pom-poms come in bags of 6.
Stickers come in sheets of 14. She wants to buy as few bags and sheets as possible and have the same number of
pom-poms and stickers so that the first students at the jamboree will all receive a free pom-pom and a sticker.
How many bags of pom-poms and sheets of stickers should she buy? She does not want to have any left over.
7
3
Bags of pom-poms
Sheets of stickers
____ 15. Christian is arranging tables for a game. He wants the same number of boys and girls at each table. Everyone
who plays the game must be at a table. The game will have 36 boys and 24 girls. What is the greatest number of
tables Cristina can make? Show your work or explain your thinking. 12 is the greatest number of tables