Pri 4 Lesson 4

Primary 4 Math Olympiad Lesson 4

By Penny Chow

Review Question from L3

What is the remainder when 12345 is divided by 11?

Ans: 3

Prime Factorization

What are prime numbers?
A prime number only have 2 factors: 1 and itself.

For example, the first few prime numbers are

2, 5, , , 13, 17,

Is 1 a prime number? How about 0?

Can you list all the even prime numbers?

Prime Factorization

Prime factorization: breaking a number down into a product of prime numbers by dividing it repeatedly by the smallest possible prime.

24

2

2

2

12

6

3

For example, the factor tree of 24 is

Using the factor tree we repeatedly divided the branch by a prime factor until all the branches are prime numbers.

Multiple Choice

Prime factorization of 12 is 2x6.

• True

• False

Prime Factorization

Use the factor tree method to find the prime factorization of the following:

1) 18

2) 32

3) 105

4) 561

Multiple Choice

Can a number have two different prime factorization?

• True

• False

Prime Factorization

Example 1: Divide these four numbers: 15, 33, 35, 77 into two groups so that the product of the numbers in the first group is equal to that of the numbers in the second group.

Prime Factorization

Example 2: Divide these six numbers: 11, 18, 33, 72, 75, 100 into two groups so that the product of the numbers in the first group is equal to that of the numbers in the second group

Prime Factorization

Example 3: Find the 3 Consecutive even numbers whose product is 13728.

Prime Factorization - LCM

Least Common Multiple (LCM) is the product the highest order of each unique prime factor between the numbers.

For example, the LCM of 54 and 84 can be found as:

Therefore, the LCM of 54 and 84 is

Prime Factorization - HCF

Use prime factorization to find the HCF of the following groups:

1) 144 and 270

2) 36, 45, and 66

Prime Factorization - LCM

Example 1: The lowest common multiples of 4 consecutive numbers are 1980. Find the product of these numbers.

Prime Factorization - LCM

Example 2: The Tan Family has 3 sons. The eldest son is 3 years older than the second son while the second son is in turn 3 years older than the youngest son. Given that the lowest common multiple of their ages is 180 and the youngest son is less than 10 years old, what is the

age of the oldest son?

Prime Factorization - HCF

Highest Common Factor (HCF) is the product the lowest order of each unique prime factor between the numbers.

For example, the HCF of 54 and 84 can be found as:

Notice that if one number doesn't have the prime factor that the other one have, it is considered a power of 0.

Therefore, the HCF of 54 and 84 is

Prime Factorization -HCF

Use prime factorization to find the HCF of the following groups:

1) 144 and 270

2) 36, 45, and 66

Prime Factorization - HCF

Example 1: A piece of paper, 375 cm by 480 cm, is to be cut into squares with no wastage. What is the length of the largest square possible, and how many of such squares will there be?

Prime Factorization - HCF

Example 2: A solid cuboid, measuring 720 mm by 450 mm by 135 mm, is to be cut into identical cubes with no wastage. What is the length of the largest cube possible, and how of such cubes will there be?

Homework

1. Find the highest common factor of 87318 and 218295.

2. What is the product of the LCM and HCF of any pair of whole numbers? How? (Hint: think about the process of doing LCM and HCF)