Prime and Composite Numbers
Grade 5 · Math · Study Guide
Understand the difference between prime and composite numbers and how to identify them.
Every whole number greater than 1 is either prime or composite. Understanding the difference helps you work with factors, multiples, and fractions.
A prime number is a whole number greater than 1 that has exactly two factors: 1 and itself. The number 7 is prime because its only factors are 1 and 7. The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, and 23. Notice that 2 is the only even prime number because all other even numbers are divisible by 2.
A composite number is a whole number greater than 1 that has more than two factors. The number 12 is composite because its factors are 1, 2, 3, 4, 6, and 12. Every composite number can be broken down into a product of prime numbers, called its prime factorization.
The number 1 is neither prime nor composite — it is a special case with only one factor.
A helpful strategy for identifying prime numbers is to check whether the number is divisible by any prime number up to its square root. If none divide evenly, the number is prime. You can also use a factor tree to find the prime factorization of a composite number by repeatedly breaking it into factor pairs until all branches end in prime numbers.
Key terms
- Prime number
- A whole number greater than 1 with exactly two factors: 1 and itself
- Composite number
- A whole number greater than 1 with more than two factors
- Factor
- A whole number that divides evenly into another number with no remainder
- Prime factorization
- Expressing a composite number as a product of its prime factors, for example 12 = 2 x 2 x 3
- Factor tree
- A diagram used to break a composite number into its prime factors by repeatedly finding factor pairs
- Divisible
- One number is divisible by another if the division results in a whole number with no remainder
Flashcards
- Is 13 prime or composite?
- Prime — its only factors are 1 and 13
- Is 24 prime or composite?
- Composite — factors include 1, 2, 3, 4, 6, 8, 12, 24
- Prime factorization of 18
- 2 x 3 x 3 (or 2 x 3²)
- Prime factorization of 30
- 2 x 3 x 5
- Why is 1 neither prime nor composite?
- 1 has only one factor (itself); prime numbers must have exactly two factors
- First 10 prime numbers
- 2, 3, 5, 7, 11, 13, 17, 19, 23, 29
- Factor tree for 36
- 36 = 4 x 9 = 2 x 2 x 3 x 3; prime factorization is 2² x 3²
Questions
Which of the following is a prime number?
- 9
- 15
- 17
- 21
Show answer
Answer: 17
17 has exactly two factors (1 and 17) so it is prime. 9 = 3x3, 15 = 3x5, and 21 = 3x7 are all composite.
The number 1 is a prime number.
Show answer
Answer: False
The number 1 has only one factor (itself). Prime numbers must have exactly two distinct factors. Therefore 1 is neither prime nor composite.
The prime factorization of 12 is 2 x 2 x ___.
Show answer
Answer: 3
12 = 2 x 6 = 2 x 2 x 3. The prime factorization of 12 is 2 x 2 x 3.
How many factors does a prime number have?
- 1
- 2
- 3
- More than 3
Show answer
Answer: 2
By definition, a prime number has exactly 2 factors: 1 and itself. No more, no fewer.
2 is the only even prime number.
Show answer
Answer: True
All even numbers are divisible by 2. The only even number that is prime is 2 itself, because all larger even numbers have at least 3 factors.
Get a personalized course on Prime and Composite Numbers built around your child.