Unit 5 : Prime numbers 

Keywords and phrases:

divisible only by 1 and itself

natural number

greater than 1

Indivisible

building blocks of n

to factor

composite number

Examples of prime numbers:

2 (the only even prime number)

3

5

7

11

13

17

19

23

29

Note: These numbers are called prime because they can only be divided by 1 and themselves without leaving a remainder.

How to find prime numbers

30

30 = 5 x 6

30 = 5 x 3 x 2

The prime factorization of 30 is:

• 30 = 2 × 3 × 5

This means that 30 can be expressed as the product of the prime numbers 2, 3, and 5.

For example, 30 is not a prime number. To understand why, let's break it down using prime factors.

Start with 30: The largest prime factor of 30 is 5 because 30 can be divided by 5 (since 5 times 6 equals 30).

Prime Factor of 5: 5 is a prime number because it can only be divided by 1 and itself.

Next, factorize 6: Now, look at 6. The largest prime factor of 6 is 3, because 3 times 2 equals 6.

Prime Factors of 3 and 2: Both 3 and 2 are prime numbers for the same reason as 5: they can only be divided by 1 and themselves.

Multiplying the Prime Factors: Therefore, when you multiply these prime numbers—5, 3, and 2—together, you get the original number: 5 × 3 × 2 = 30.

This process of breaking down a number into its prime factors is called prime factorization.

How to find prime numbers

25

25 = 5 x 5

25 = 5 × 5: This means 25 is not a prime number. Instead, it is a composite number (a number with more than two factors). The prime factorization of 25 is 5 × 5.

Now, let's factorize the number 25.

The largest (and only) prime factor of 25 is 5 because 25 can be divided by 5 (since 5 times 5 equals 25).

Prime Factor of 5: 5 is a prime number because it can only be divided by 1 and itself.

Therefore, the prime factorization of 25 is 5 × 5.