Ibn Khuldoon National School – Middle School
Mathematics Department – Grade 7
Unit 1: Numbers
By the end of this Unit I will be able to:
1. Find GCF, LCM and square and cubic roots using
the prime factorization method.
Name :________________________
Section :___________
1
Divisibility Rules
A number is divisible by ​two​ if it is an even number.
(Ex.: it ends in 0, 2, 4, 6, or 8.)
A number is divisible by 5 if it ends in 5 or 0.
(Ex: it ends in 0 or 5)
A number is divisible by 10 if it ends in 0.
A number is divisible by 3 if the ​sum​ ​of​ ​the​ ​digits​ is divisible by 3. (Ex.: 324 is divisible by 3 because
3 + 2 + 4 = 9, and 9 is divisible by 3.)
A number is divisible by 9 if the sum on the digits is divisible by 9.
(Ex.: 423 is divisible by 9 because
4 + 2 + 3 = 9, and 9 is divisible by 9.)
A number is divisible by ​6​ if it is divisible by
​both​ ​ ​2​ ​and​ ​3​.
A number is divisible by ​4​ if the ​last two digits ​are divisible by 4.
2
Factors
Practice 1: Determine whether each number is prime or composite.
1.
34
2.
37
3.
77
4.
89
5.
87
6.
67
Prime Factorization
Practice 2: Write each of the following numbers as a product of its prime factors in index
form.
1.
16
2.
72
3.
80
3
4.
490
5.
225
6.
130
7.
105
8.
60
9.
144
4
10.
1140
11.
11340
12.
18900
5
Practice 3: Tell whether each of the following numbers is factor of 18900 or not.
1.
12
2.
70
3.
24
4.
63
5.
55
6
Lowest common multiple and Highest common factor
Practice 4: find the GCF (HCF) of each of the following numbers.
1. 12, 18
2. 60, 96
3. 120, 150
4. 27, 99, 36
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Practice 5: Find the LCM of each of the following numbers
1. 9 and 12
2. 120 and 150
3. 60 and 96
4. 4, 6 and 7
8
​Practice 6:
Jena thinks of two numbers. She says:
“The Highest Common Factor (HCF) of my two numbers is 3,
The Lowest Common Multiple (LCM) of my two numbers is 45”
Write down two numbers that Jena could be thinking of.
Practice 7:
Two neon lights are turned on at the same time. One blinks every 4 seconds and the other
blinks every 6 seconds. In 60 seconds, how many times will they b
​ link at the same time​?
Practice 8:
The school cafeteria serves tacos every 9​th​ day and cheeseburgers every 12​th​ day. If tacos and
cheeseburgers are both on today’s menu, how many days will it be before they are both on the menu
again?
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Practice 9:
Local food shops are assembling fruit baskets for donation. Each box must have the same number of
each kind of fruits. You are one of the volunteers who are working to assemble the baskets. The goal is
to have as many baskets as possible with no fruits leftover and you had 24 apples, 40 oranges and 32
bananas.
a. How many baskets you can make? (Remember that the baskets must be identical)
b. How many fruits of each kind you will put in each basket?
Practice 10:
A group of selected middle school students from grades 6, 7 and 8 are chosen for a community service
event. If 36 students are selected from grade 6, 48 students are selected from grade 7 and 60 students
are selected from grade 8. The school leader wants to divide this group of students into different teams.
Each team must include students from each grade level and different teams must have the same
number of grade 6 students, grade 7 students and grade 8 students.
a. What is the largest number of teams the leader can create?
b. 3 more similar teams of the same structure are needed to serve in different areas, how many
more students from grade 7 do we need?
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Practice 11:
Two satellites are put into orbit over the same location at the same time. One orbits the earth every 24
hours, while the second completes an orbit every 18 hours. How much time will elapse before they are
once again over the same location at the same time?
11
Roots
Practice 12: ​Use the Prime Factorization method to decide if these numbers are perfect squares
and to find the square roots of those that are perfect squares.
1. 225
2. 400
3. 360
4. 484
5. 280
Practice 13: Evaluate using prime factorization
1.
√441
2.
√1024
12
3
3.
√216
4.
√1728
5.
√2744
6.
√625
7.
√1296
3
3
4
4
4
Practice 14: ​Explain why √2744 is not a whole number.
Practice 15: ​Explain why 7 <
√51
< 8
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