This document provides an overview of factors, exponents, multiples, prime numbers, and finding the least common multiple (LCM) of numbers. It includes examples of listing the factors of numbers, identifying prime and composite numbers, using common multiples to determine how many food packages to purchase to avoid leftovers, and calculating the LCM of sets of numbers. The document is intended to teach mathematical concepts and includes practice problems for students.

1. MATH Grade 7
Chapter 1.1 - Factors and Exponents

2. 1. What can Kyle pay for using only $2 coins?
2. What can he pay for using only $5 bills? What can he pay for using only $10 bills?
3. Which prices require Kyle to use more than one type of bill or coin? Explain why.
4. Suppose that the price of another item is a whole number ending in the digit 0. Can Kyle use
only one type of bill or coin to pay this amount? Explain. Can he use more than one type of bill or
coin? Explain.
5. Write a price that is greater than $100 and that someone can pay using only one type of bill or
coin.
6. Write a price that is greater than $100 and that somone cannot pay using only one type of bill or
coin.

3. Do you know - Factor, Multiple and Prime Numbers?

4. Factor
Factors are numbers you can multiply together to get another number:
A number can have MANY factors!
What are factors of 12? You try!

5. Factor of 12
3 and 4 are factors of 12, because 3 × 4 = 12.
Also 2 × 6 = 12 so 2 and 6 are also factors of 12.
And 1 × 12 = 12 so 1 and 12 are factors of 12 as well.
So 1, 2, 3, 4, 6 and 12 are all factors of 12
And -1, -2, -3, -4, -6 and -12 also, because multiplying negatives makes a positive

6. Practise:
1. Factors of 4
2. Factors of 8
3. Factors of 20
4. Factors of 100
5. Factors of 13

7. Multiples
- Result of multiplying a number by an integer (next slide: what is an integer)
- Examples:
- • 12 is a multiple of 3, as 3 × 4 = 12
- • −6 is a multiple of 3, as 3 × −2 = −6
- • But 7 is NOT a multiple of 3

8. Integer
- A number with no fractional part (no decimals) or whole numbers
- Includes:
- • the counting numbers {1, 2, 3, ...},
- • zero {0},
- • and the negative of the counting numbers {-1, -2, -3, ...}
- Which of these numbers are integers: ½, 3.5, 8.0, 4, -5.1, -⅗ , 1 ?

9. Prime Numbers
A number that can only be evenly divided (produce an integer) by 1 or itself
Any number you can think of?

10. Here is a list of all the prime numbers up to 100:
- Any patterns you notice?

11. Composite Numbers
- Opposite of prime numbers. So what is composite numbers?

12. Composite Numbers
A whole number that can be divided evenly by numbers other than 1 or itself.
Example: 9 can be divided evenly by 3 (as well as
1 and 9), so 9 is a composite number.
But 7 cannot be divided evenly (except by 1
and 7), so is NOT a composite number (it is a
prime number).

13. Some Grade 7 students are planning a hot-dog fundraiser sale at a masjid. Based
on the last time they held the event, they expect to sell 100 hot dogs. The local
grocery store sells hot dogs in pack ages of 12 and buns in pack ages of 8.
How many packages of wieners and buns should the students buy if they want to
make about 100 hot dogs, with no wieners or buns left over?

14. Calculate the number of wieners contained in 1, 2, 3, 4,
and 5
packages by listing multiples of 12.
Calculate the number of buns contained in 1, 2, 3,
4, and 5 packages
by listing multiples of 8.
Circle multiple that is the least number

15. LCM (Least Common Multiple)
Least common multiple (LCM) the least whole number that has two or more given
numbers as factors; for example, 12 is the least common multiple of 4 and 6

16. Example 1: Finding the least common multiple of two numbers
What is the LCM of 5 and 8?
Thaznim’s Solution:
5, 10, 15, 20, 25, 30, 35, 40, 45, …
8, 16, 24, 32, 40, …
The LCM of 5 and 8 is 40.
The steps she took:
I listed multipl es of each number.
Then I circled the least number comm on to both lists.

17. Example 2: Finding the LCM of three numbers
Stephen is training for the three events in a triathalon. He runs every second day,
swims every third day, and rides a bicycle every fifth day. How many times during
the month of April will he have to practise all three events on the same day?
Ahmed ’s Solution:
2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30
3, 6, 9, 12, 15, 18, 21, 24, 27, 30
5, 10, 15, 20, 25, 30
Only one time in April will Stephen have to
practise all three events on the same day
The steps he took:
I listed the multiples of 2, 3, and 5
to 30.
The LCM is 30.
On April 30th, Stephen will have to
practise all three events.

18. Example 3: Using common multiples
Khadijah plans to make roll-ups for a party. She rolls a slice of meat with a slice of cheese. Each meat
package has 10 slices. Each cheese package has 12 slices. How many packages of each should she buy
so that there are no leftovers?
Khadijahs Solution:
10, 20, 30, 40, 50, 6 0 , 70, 80, 90, 100, 110, 1 2 0 , 130, …
12, 24, 36, 48, 6 0 , 72, 84, 96, 108, 1 2 0 , …
60 / 10 slices of meat = 6 packages
60 / 12 slices of cheese = 5 packages
120 / 10 slices of meat = 12 packages
120 / 12 slices of cheese = 10 packages
The least amount I should buy is 6 packages of
meat and 5 packages of cheese.

19. The steps she took:
- I listed multiples of 10 and 12.
- I circled the common multiples.
- 60 is the LCM.
- I could buy 60 slices of meat and 60 slices of cheese to make 60 roll-ups. That’s 6 packages of meat and 5
packages of cheese. Or, I could buy 120 slices of each to make 120 roll-ups. That’s 12 packages of meat
and 10 packages of cheese.