Identify even, odd and prime numbers

Odd numbers are counting numbers that leave a remainder of 1 when divided by 2.

When you try to group counters into pairs, odd numbers will always have one counter left over. The last digit of an odd number is 1, 3, 5, 7, or 9.

How to identify an odd number

Look at the last digit:

• If it ends in 1, 3, 5, 7, or 9 → the number is odd.

Worked examples

Example 2: Write all odd numbers from the following list: 38, 49, 87, 96, 105, 254, and 281.

Answer

The odd numbers from the list are: 49, 87, 105, and 281.

A prime number is a counting number that has exactly two different factors: 1 and itself.

For example, 5 is a prime number because its only factors are 1 and 5. No other number divides 5 evenly.

Important notes

• 1 is NOT a prime number. It has only one factor (itself), but a prime number must have exactly two factors.
• 2 is the only even prime number. All other even numbers have 2 as a factor, so they are not prime.
• All prime numbers (except 2) are odd numbers.

How to find prime numbers up to 100

1. List all numbers from 1 to 100.
2. Circle 2, then cross out all multiples of 2.
3. Circle 3, then cross out all multiples of 3.
4. Circle 5, then cross out all multiples of 5.
5. Circle 7, then cross out all multiples of 7.
6. The numbers that are circled (except 1) are prime.

Worked examples

Example 3: List all prime numbers less than 20.

Answer

The prime numbers less than 20 are: 2, 3, 5, 7, 11, 13, 17, and 19.

Example 4: Write all prime numbers between 101 and 120.

Answer

Testing each number: 103, 107, 109, and 113 are not divisible by 2, 3, 5, or 7.

So the prime numbers between 101 and 120 are: 103, 107, 109, and 113.

In everyday life in Tanzania, you use even, odd, and prime numbers without realizing it. For example, when selling fruits at the market, you might group mangoes in pairs (even numbers) to price them easily — if each pair costs TSh 1,000, then 8 mangoes (an even number) cost TSh 4,000. Understanding prime numbers helps when dividing things equally among friends, like sharing 11 mandazi (a prime number) where you cannot split them evenly into equal whole groups.