Prime numbers hiding in times tables

Quick answer

Prime numbers only appear in the 1 row and their own row in a times table grid because they can only be made by multiplying 1 and themselves. For example, 7 is a prime number, so it only appears in the 1 row (1 x 7 = 7) and the 7 row (7 x 1 = 7).

Learning outcome

By the end of this page, you will understand why prime numbers only appear in the 1 row and their own row in a times table grid.

• You can explain what makes a prime number.
• You can find prime numbers in a times table grid.
• You can identify which rows in a times table grid show prime numbers.
• You can create your own times table grid and spot prime numbers.

Why this matters

Understanding how prime numbers appear in times tables helps you see patterns in maths. It also makes multiplication easier to understand and helps you find factors quickly. This is useful in games, puzzles, and even in real life when you need to share things equally or find the best way to group items.

Prime numbers are special and show up in many places, from secret codes to computer security. Learning how they work in times tables is a fun way to start your journey into the world of number patterns.

How it works

Let's think about what a prime number is first:

1. A prime number is a number that has only two factors: 1 and itself.
2. For example, 5 is a prime number because its only factors are 1 and 5 (1 x 5 = 5).
3. When we make a times table grid, we multiply numbers together.
4. If a number is prime, it can only be made by multiplying 1 and itself.
5. So, in a times table grid, the prime number will only appear in the row for 1 and its own row.

Examples you can see

Let's look at a small times table grid to see how this works:

Look at the prime numbers in this grid:

• 2 is prime, so it only appears in the 1 row and the 2 row.
• 3 is prime, so it only appears in the 1 row and the 3 row.
• 5 is prime, so it only appears in the 1 row and the 5 row.
• 7 is prime, so it only appears in the 1 row and the 7 row.

Notice how each prime number only shows up twice in the grid – once in the 1 row and once in its own row.

Try it as a mini adventure

Let's go on a Prime Number Hunt!

Imagine you are a detective looking for prime numbers in a big times table grid. Your mission is to find all the prime numbers between 1 and 20 and mark the rows where they appear.

Start with a list of numbers from 1 to 20:

1. 1 (not prime)
2. 2 (prime)
3. 3 (prime)
4. 4 (not prime)
5. 5 (prime)
6. 6 (not prime)
7. 7 (prime)
8. 8 (not prime)
9. 9 (not prime)
10. 10 (not prime)
11. 11 (prime)
12. 12 (not prime)
13. 13 (prime)
14. 14 (not prime)
15. 15 (not prime)
16. 16 (not prime)
17. 17 (prime)
18. 18 (not prime)
19. 19 (prime)
20. 20 (not prime)

Now, draw a grid like the one above, but only up to 20. Mark the prime numbers and see which rows they appear in. You'll notice that 11 appears in the 1 row and the 11 row, 13 appears in the 1 row and the 13 row, and so on.

Common mistakes

• Mistake: Thinking that 1 is a prime number.
  Why it happens: Children often forget that 1 only has one factor, which is itself.
  Fix: Remember that prime numbers must have exactly two factors: 1 and themselves. Since 1 only has one factor, it is not prime.
• Mistake: Thinking that 2 is the only even prime number.
  Why it happens: Some children think all even numbers are not prime.
  Fix: 2 is the only even prime number because all other even numbers can be divided by 2, so they have more than two factors.
• Mistake: Seeing 12 in the 3 row and thinking it's a prime number.
  Why it happens: Children might not know that 12 can be made by multiplying 2 x 6 or 3 x 4.
  Fix: 12 is not prime because it has more than two factors: 1, 2, 3, 4, 6, and 12.

Parent and carer guide

Help your child understand prime numbers by:

1. Using everyday examples like sharing candies equally or arranging toys in rows.
2. Playing a game where you ask them to find prime numbers in a grid.
3. Encouraging them to make their own times table grids and mark prime numbers.
4. Reinforcing that 1 is not prime, and that 2 is the only even prime number.
5. Practicing multiplication facts to help them see patterns.

Remember, this is a new concept, so don't worry if it takes time to understand. Keep it fun and use lots of visual aids and hands-on activities.

Practice questions

1. Which numbers are prime between 1 and 12?
   Answer: 2, 3, 5, 7, 11
2. Where do you find the number 13 in a times table grid?
   Answer: In the 1 row and the 13 row
3. Why does 15 not appear in the 15 row of a times table grid?
   Answer: Because 15 is not a prime number. It has factors 1, 3, 5, and 15.
4. What is the smallest prime number?
   Answer: 2
5. Which rows in a times table grid show prime numbers?
   Answer: The 1 row and the row of the prime number itself

FAQ

What is a prime number?

A prime number is a number that has exactly two factors: 1 and itself. For example, 7 is prime because its only factors are 1 and 7.

Why don't prime numbers appear in other rows?

Because prime numbers can only be made by multiplying 1 and themselves. So they only appear in the 1 row and their own row in a times table grid.

Are all odd numbers prime?

No, not all odd numbers are prime. For example, 9 is odd but not prime because it can be made by multiplying 3 x 3.

Can you find prime numbers in a 12 times table grid?

Yes! You can find prime numbers in a 12 times table grid by looking at the 1 row and the rows of the prime numbers themselves (2, 3, 5, 7, 11).

What is the biggest prime number?

There is no biggest prime number. Prime numbers go on forever, and mathematicians are still discovering new ones!