Vocab/Notes
True or False: A prime factorization of a number is unique
True!
What is the prime factorizations of 24?
2 x 2 x 2 x 3
GCF(36,12)
12
LCM(5,15)
15
Kiara baked 30 oatmeal cookies and 48 chocolate chip cookies to package in plastic containers for her friends at school. She wants to divide the cookies into identical containers so that each container has the same number of each kind of cookie. If she wants each container to have the greatest number of cookies possible, how many plastic containers does she need?
6 containers
What is a prime number?
A number whose only factors are 1 and itself
What is the prime factorization of 19?
19 x 1
GCF(42,48)
6
LCM(7,12)
84
Hector is dividing students into groups for a nature hike. He wants to divide the 21 6th-graders and 56 7th-graders so that each group has the same number of both 6th- and 7th-graders. Into how many groups can the students be divided?
7 groups
When you are asked to divide quantities up into even groups, what are you looking for?
Factors
What is prime factorization of 63?
3 x 3 x 7
GCF(8,12,48)
4
LCM(30,18)
90
Pencils come in packages of 10. Erasers come in packages of 12. Phillip wants to purchase the smallest number of pencils and erasers so that he will have exactly 1 eraser per pencil. How many packages of pencils and erasers should Phillip buy?
6 of pencils and 5 of erasers
How can you tell if the least common multiple will be less than the product of the two numbers? (i.e. will the LCM of 10 and 8 be 80? or less than 80? How do you know?)
What is prime factorization of 105?
3 x 5 x 7
GCF(65, 104)
13
LCM(3,8,10)
120
At the middle school, the bell rings every 40 minutes to tell the students to change classes. Across the street, the clock above city hall chimes every 30 minutes. Both the school bell and the clock ring at noon. When will both bells ring again at the same time?
120min (at 2pm)
When a question asks for you to synch up a cycle (when will things occur at the same time), what are you looking for?
Multiples
What is the prime factorization of 128?
27
GCF(18,36,90)
18
LCM(12,15,18)
180
Yuko creates food baskets to give to local families. He has 192 corn bread muffins, 96 cans of vegetables, and 64 boxes of stuffing mix. What is the greatest number of baskets Yuko can create if he wants to use all of the items and have the same number of each item in each basket?
32 food baskets (Each basket will contain 6 corn bread muffins, 3 cans of vegetables, and 2 boxes of stuffing mix.)