UNDERSTANDING THE FACTORS OF NUMBERS - JSS2 Mathematics Lesson Note

What are Factors?

Factors are numbers that you can multiply together to get another number. For example, if you multiply 2 and 3, you get 6, so 2 and 3 are factors of 6. Every number has factors, and some numbers have many factors.

Finding Factors

To find the factors of a number, you need to see which numbers can divide into it without leaving a remainder. For instance, the factors of 12 are:

1 (because 1 × 12 = 12)

2 (because 2 × 6 = 12)

3 (because 3 × 4 = 12)

4 (because 4 × 3 = 12)

6 (because 6 × 2 = 12)

12 (because 12 × 1 = 12)

So, the factors of 12 are 1, 2, 3, 4, 6, and 12.

Prime Factors

Prime numbers are numbers greater than 1 that have no factors other than 1 and themselves. Examples of prime numbers are 2, 3, 5, 7, and 11. When you express a number as a product of its prime factors, you break it down into the smallest prime numbers that multiply to give the original number.

Finding Prime Factors

To find the prime factors of a number, you keep dividing the number by the smallest prime number until you end up with 1. Let's use the number 60 as an example:

Start with the smallest prime number, 2. Divide 60 by 2:

60÷2=30 (2 is a prime factor)

Divide 30 by 2 again:

30÷2=15 (2 is a prime factor)

Now, 15 is not divisible by 2, so move to the next smallest prime number, which is 3. Divide 15 by 3:

15÷3=5 (3 is a prime factor)

Finally, 5 is a prime number, so we stop here:

5÷5=1 (5 is a prime factor)

So, the prime factors of 60 are 2, 2, 3, and 5.

We can write this as: 60=2×2×3×5

Highest Common Factor (HCF)

The highest common factor (HCF), also known as the greatest common divisor (GCD), is the largest number that can divide two or more numbers without leaving a remainder. To find the HCF, you can use the prime factors of the numbers.

Finding the HCF Using Prime Factors

• Let's find the HCF of 60 and 48.
• Find the prime factors of 60: 60=2×2×3×5
• Find the prime factors of 48: 48=2×2×2×2×3
• Identify the common prime factors: Both 60 and 48 have the prime factors 2, 2, and 3 in common.
• Multiply the common prime factors: 2×2×3=12
• So, the HCF of 60 and 48 is 12

 

Example of Finding the HCF of Three Numbers

Let's find the HCF of 24, 36, and 60.

• Find the prime factors of each number:
  • 24=2×2×2×3
  • 36=2×2×3×3
  • 60=2×2×3×5

Identify the common prime factors:

• All three numbers have the prime factors 2, 2, and 3 in common.

Multiply the common prime factors:

• 2×2×3=12
• So, the HCF of 24, 36, and 60 is 12.