Prime, Composite & Square Numbers
Sort: Prime or Composite?
Sort each number into the correct column. Remember: a prime number has exactly 2 factors (1 and itself).
Sort More Numbers: Prime or Composite?
Sort each number. Is it prime or composite?
Spot the Prime Number
Circle the prime number in each group.
Which is prime?
Which is prime?
Which is prime?
Which is prime?
Find the Prime
Circle the prime number in each group.
Which is prime?
Which is prime?
Which is prime?
Which is prime?
Spot the Composite Number
Circle the composite number in each group.
Which is composite?
Which is composite?
Which is composite?
Which is composite?
Match Numbers to Factor Counts
Draw a line to match each number to how many factors it has.
List the Factors
List all the factors of each number. Then say if it is prime or composite.
Factors of 18: ___ Prime or Composite? ___
Factors of 23: ___ Prime or Composite? ___
Factors of 36: ___ Prime or Composite? ___
Factors of 29: ___ Prime or Composite? ___
Write All the Primes
Write all the prime numbers in each range.
Prime numbers between 1 and 20: ___
Prime numbers between 20 and 40: ___
Prime numbers between 40 and 60: ___
Is 1 Prime or Composite?
Circle the correct answer.
The number 1 is:
The number 2 is:
The number 0 is:
Match Square Numbers
Draw a line to match each multiplication to its square number.
Match More Square Numbers
Draw a line to match each multiplication to its square number.
Square Number Sequence
Fill in the missing square numbers.
More Square Numbers
Fill in the missing square numbers in the sequence.
Find the Square Root
Write the square root of each number. The first one is done for you: √25 = 5.
√36 = ___
√64 = ___
√81 = ___
√144 = ___
√100 = ___
More Square Roots
Write the square root of each number.
√1 = ___
√4 = ___
√9 = ___
√16 = ___
√49 = ___
√121 = ___
Is It a Square Number?
Circle YES or NO for each number.
Is 25 a square number?
Is 30 a square number?
Is 49 a square number?
Is 50 a square number?
Is 64 a square number?
Is 72 a square number?
Sort: Square or Not Square?
Sort each number into the correct column.
Square Number Calculations
Calculate each square number.
6² = ___
9² = ___
11² = ___
15² = ___
20² = ___
Sort: Prime, Composite or Square?
Sort each number. Some numbers may fit more than one category — choose the best fit.
Prime, Composite or Square?
Circle the correct classification for each number.
49 is:
37 is:
24 is:
64 is:
Number Properties Investigation
Answer each question about number properties.
Name a number that is both square and odd: ___
Name a number that is both composite and even (but not square): ___
What is the smallest prime number? ___
Name two consecutive composite numbers: ___ and ___
True or False? Number Properties
Circle TRUE or FALSE for each statement.
All even numbers are composite
1 is a prime number
Every square number has an odd number of factors
The number 2 is the only even prime number
More True or False
Circle TRUE or FALSE for each statement.
All odd numbers are prime
The sum of two prime numbers is always even
Every square number is composite
There are more composite numbers than prime numbers between 1 and 50
Prime Factor Trees
Write each number as a product of its prime factors.
30 = ___ × ___ × ___
24 = ___ × ___ × ___ × ___
45 = ___ × ___ × ___
60 = ___ × ___ × ___ × ___
Challenge: Number Puzzles
Solve each puzzle about prime, composite and square numbers.
I am a square number between 30 and 50. What am I? ___
I am a prime number between 40 and 50. What am I? (There are two answers.) ___
I am a square number and also an even number less than 20. What could I be? ___
I am the sum of the first four square numbers (1 + 4 + 9 + 16). Am I prime or composite? ___
Explain Your Thinking
Answer each question and explain your reasoning.
Why is 1 not considered a prime number?
Why is 2 the only even prime number?
Can a square number also be prime? Explain why or why not.
Home Activity: Number Detective
Explore prime, composite and square numbers at home!
- 1Write all prime numbers between 1 and 50. How many did you find?
- 2Use tiles or counters to prove that 16 is a square number by arranging them in a perfect square.
- 3Find a composite number and list all of its factors.
- 4Challenge someone at home: give them a number and ask if it is prime, composite, or square.
- 5Make a prime number sieve (Sieve of Eratosthenes) on a 1-100 grid.
Square Number Sequence Extended
Continue the square number sequence.
Factors and Divisibility
List all factors and check divisibility.
Factors of 48: ___. How many factors does 48 have? ___
Is 42 divisible by 6? ___. By 7? ___. By 9? ___.
Factors of 100: ___. How many factors? ___
What is special about the number of factors of a square number? ___
Divisibility Rules
Circle YES if the number is divisible by the given number, NO if not.
Is 126 divisible by 3?
Is 245 divisible by 5?
Is 84 divisible by 4?
Is 97 divisible by 7?
Sort by Divisibility
Sort each number into the correct column.
Prime Factorisation Extended
Write each number as a product of prime factors using index notation.
36 = 2² × ___
72 = 2³ × ___
100 = 2² × ___
48 = 2⁴ × ___
Match Number to Prime Factorisation
Draw a line to match each number to its prime factorisation.
HCF and LCM (Extension)
Find the Highest Common Factor (HCF) and Lowest Common Multiple (LCM) of each pair.
HCF of 12 and 18: ___. LCM of 12 and 18: ___
HCF of 15 and 25: ___. LCM of 15 and 25: ___
HCF of 8 and 20: ___. LCM of 8 and 20: ___
Odd and Even Square Numbers
Circle the correct answer.
4 (= 2²) is:
9 (= 3²) is:
16 (= 4²) is:
25 (= 5²) is:
What is the pattern? Even squares are:
Twin Primes and Prime Gaps (Extension)
Twin primes are pairs of primes that differ by 2.
Name two pairs of twin primes between 1 and 20: ___
Name two pairs of twin primes between 20 and 50: ___
Are there twin primes near 100? ___
Goldbach's Conjecture (Extension)
Goldbach's Conjecture: every even number > 2 is the sum of two primes. Test it!
10 = ___ + ___
16 = ___ + ___
28 = ___ + ___
50 = ___ + ___
Prime Numbers in Ranges
This graph shows how many primes are in each range of 10. Answer the questions.
| 1–10 | |
| 11–20 | |
| 21–30 | |
| 31–40 | |
| 41–50 |
Which range has the most primes?
How many primes are there between 1 and 50 in total?
What trend do you notice as numbers get larger?
Square Number Digit Patterns
Check the units digit of each square number. Tally how many end in each digit.
| Item | Tally | Total |
|---|---|---|
Ends in 0 | ||
Ends in 1 | ||
Ends in 4 | ||
Ends in 5 | ||
Ends in 6 | ||
Ends in 9 |
Primes and Perfect Squares Together
Investigate the relationship between primes and square numbers.
Can a prime number be a perfect square? Explain: ___
List all perfect squares up to 200: ___
Between which two square numbers do most primes lie below 100? ___
Indices and Square Numbers (Extension: includes cubes and higher powers)
Circle the correct answer.
3² = ?
4³ = ?
2⁵ = ?
5² = ?
Match Power to Value (Extension)
Draw a line to match each index expression to its value.
Order Powers and Square Numbers (Extension)
Sort these values from smallest to largest.
Cube Numbers (Extension)
A cube number is n × n × n (or n³). Calculate each cube number.
1³ = ___
2³ = ___
3³ = ___
4³ = ___
5³ = ___
Number Properties Investigation 2
Investigate and explain these number properties.
What is the only even prime? ___. Why can no other even number be prime? ___
Write the first 6 composite numbers: ___
What do all square numbers have in common with their factor count? ___
Applying Number Properties
Use your knowledge to solve these problems.
A square tile pattern has 144 tiles. How many tiles make each side of the square? ___
You want to share 97 books equally between groups. Why is 97 difficult to share equally? ___
Which numbers between 1 and 50 are both square and even? ___
Modelling Square Numbers
Count the objects that could be arranged in a perfect square.
Writing About Number Types
Write a clear explanation for each.
Explain what makes a number prime in your own words: ___
Describe the difference between a square number and a cube number: ___
Number Patterns with Squares and Primes
Explore these patterns.
What do 1, 4, 9, 16, 25 all have in common? ___
Add consecutive odd numbers starting from 1: 1, 1+3=4, 1+3+5=9. What do you notice? ___
Use this pattern to predict the 6th square number without multiplying: ___