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Maths Facts

Why 1 is not prime

Explain the modern definition of prime numbers with factor pairs.

Quick answer

1 is not prime because it only has one factor, not two factors like prime numbers must have.

Learning outcome

By the end of this page, you will understand why 1 is not a prime number and be able to explain what makes a number prime. Success signs:
  • You can name at least two factors of any number
  • You can explain why 1 is different from other numbers
  • You can identify prime numbers up to 20
  • You can show that 1 only has one factor

Why this matters

Understanding why 1 is not prime helps us make sense of how numbers work in maths. It's like learning the rules of a game – if we know the rules, we can play better and solve problems more easily. This idea helps us understand how numbers are built, which is important for bigger maths like fractions, multiplication, and division. When you know that 1 is not prime, you'll be ready to understand how prime numbers help us break down bigger numbers into their simplest parts.

How it works

To understand why 1 is not prime, we first need to know what a prime number is. A prime number is a number that:
  1. Is greater than 1
  2. Has exactly two factors: 1 and itself
Let's think about factors. Factors are numbers that we can multiply together to make another number. For example, 6 can be made by multiplying 2 and 3 (2 × 3 = 6). So, 2 and 3 are factors of 6. Now, let's look at 1. What numbers can we multiply together to get 1? We can only do 1 × 1 = 1. So, 1 only has one factor pair: 1 and 1. But prime numbers must have exactly two different factors. That's why 1 is not prime.

Examples you can see

Let's look at some numbers and their factors to understand better:
Number Factors Is it prime?
1 1 No
2 1, 2 Yes
3 1, 3 Yes
4 1, 2, 4 No
5 1, 5 Yes
6 1, 2, 3, 6 No
Let's imagine you're making groups of toys. If you have 1 toy, you can only make 1 group with 1 toy in it. That's only one way to group it. But if you have 6 toys, you can make:
  • 1 group of 6 toys
  • 2 groups of 3 toys each
  • 3 groups of 2 toys each
  • 6 groups of 1 toy each
That's four ways to group 6 toys. That's why 6 is not prime – it has more than two factors.

Try it as a mini adventure

Adventure: The Prime Number Quest You are on a treasure hunt in a magical land where numbers are friends. Your goal is to find the prime number friends, but first, you must learn what makes a number a prime friend. You meet a number called 1. "Hello," says 1. "I'm the smallest number, but I'm not a prime friend." "Why not?" you ask. "Because I only have one friend," 1 says. "My only factor is myself. Prime friends must have exactly two friends – 1 and themselves." You meet 2. "I'm a prime friend!" says 2. "I have two friends: 1 and 2." You meet 3. "I'm also a prime friend!" says 3. "I have two friends: 1 and 3." You meet 4. "I'm not a prime friend," says 4. "I have three friends: 1, 2, and 4." You meet 5. "I'm a prime friend!" says 5. "I have two friends: 1 and 5." You meet 6. "I'm not a prime friend," says 6. "I have four friends: 1, 2, 3, and 6." You continue your quest and find that 7, 11, 13, 17, and 19 are also prime friends. But 1 stays behind because it only has one factor. It's special, but not a prime friend.

Common mistakes

  • Mistake: Thinking that 1 is prime because it's a number
    Why it happens: Children might think that any number that's not 0 or 2 is prime.
    Fix: Remember that prime numbers must have exactly two different factors, and 1 only has one factor.
  • Mistake: Counting 1 as a prime number when listing primes
    Why it happens: Kids often forget that 1 is special and different from other numbers.
    Fix: Always remember that 1 is not prime, even though it's the first number.
  • Mistake: Believing that 1 is prime because it's "odd"
    Why it happens: Confusing prime with odd numbers.
    Fix: Remember that being odd doesn't make a number prime. 9 is odd but not prime because it has more than two factors.

Parent and carer guide

Parents and carers can help by:
  • Using everyday objects to show how factors work. For example, use 6 counters to show that 6 can be grouped as 1×6 or 2×3.
  • Playing the "Prime or Not Prime" game. Say a number and ask if it's prime. For example, "Is 7 prime?" (Yes!) "Is 1 prime?" (No!)
  • Reinforcing that prime numbers have exactly two factors – 1 and themselves.
  • Being patient if your child is confused. It's okay to say "I don't understand why 1 is not prime" – that's normal!
  • Using visual aids like arrays or factor trees to show how numbers break down.

Practice questions

  1. What are the factors of 1?
  2. Does 1 have exactly two factors?
  3. Is 1 a prime number? Why or why not?
  4. What are the factors of 2?
  5. Is 2 a prime number? Why or why not?
  6. What are the factors of 3?
  7. Is 3 a prime number? Why or why not?
  8. What are the factors of 4?
  9. Is 4 a prime number? Why or why not?
  10. Why is 1 not prime?
Answers:
  1. The factors of 1 are 1.
  2. No, 1 does not have exactly two factors.
  3. No, 1 is not a prime number because it only has one factor, not two.
  4. The factors of 2 are 1 and 2.
  5. Yes, 2 is a prime number because it has exactly two factors.
  6. The factors of 3 are 1 and 3.
  7. Yes, 3 is a prime number because it has exactly two factors.
  8. The factors of 4 are 1, 2, and 4.
  9. No, 4 is not a prime number because it has more than two factors.
  10. 1 is not prime because it only has one factor, not two like prime numbers must have.

FAQ

Why is 1 not a prime number?

1 is not prime because it only has one factor, which is itself. Prime numbers must have exactly two different factors: 1 and the number itself.

Can 1 be a factor of any number?

Yes, 1 is a factor of every number because any number multiplied by 1 equals itself.

Are there any other numbers like 1 that are not prime?

Yes, 0 is not prime because it has an infinite number of factors, and composite numbers like 4, 6, 8, 9, 10 are not prime because they have more than two factors.

Why do mathematicians say that 1 is special?

1 is special because it's the multiplicative identity – any number multiplied by 1 stays the same. But it's not prime because it doesn't meet the rule for prime numbers.

How can I remember that 1 is not prime?

Remember that prime numbers must have exactly two different factors. Since 1 only has one factor (itself), it's not prime. You can also think of it as: "1 is not prime because it only has one friend."