Prime and Composite Numbers in Maths
Grade 7 Questions With Detailed Solutions

What are prime and composite numbers in maths? This page provides Grade 7 maths questions along with step-by-step solutions. Click the arrow below each question to reveal the detailed explanation and build a strong mathematical foundation.

Definitions: Prime vs. Composite

Prime Numbers

A prime number is a whole number greater than 1 that can only be evenly divided by 1 and itself.

Examples: 2, 3, 5, 7, 11... are prime numbers. If you try to divide them by whole numbers other than 1 or themselves, the remainder will not be zero.

Composite Numbers

A composite number is a whole number greater than 1 that can be evenly divided by 1, itself, and other numbers.

Examples: 4, 6, 8, 12... are composite numbers because they have multiple factors:

Practice Questions

  1. Which of the following numbers are prime?
    1, 6.3, 11, 14, 13, 21, 23, $\dfrac{4}{5}$, 100, 123
    View Solution

    The following are prime numbers:

    • 11, 13, 23: Each of these is a whole number greater than 1, and is divisible by 1 and itself only.

    The following are NOT prime numbers:

    • 1: By definition, a prime number must be greater than 1.
    • 6.3: It is a decimal number, not a whole number.
    • 14: Divisible by 1, 2, 7, and 14.
    • 21: Divisible by 1, 3, 7, and 21.
    • $\mathbf{\dfrac{4}{5}}$: It is a fraction, not a whole number.
    • 100: Divisible by 1, 2, 4, 5, 10, etc.
    • 123: Divisible by 1, 3, 41, and 123 (Hint: 1+2+3=6, and since 6 is divisible by 3, 123 is also divisible by 3).
  2. Which of the following numbers are composite?
    1, 8.4, 15, 13, $\dfrac{9}{2}$, 24, 33
    View Solution

    The following are composite numbers:

    • 15: Divisible by 1, 3, 5, and 15.
    • 24: Divisible by 1, 2, 3, 4, 6, 8, 12, and 24.
    • 33: Divisible by 1, 3, 11, and 33.

    The following are NOT composite numbers:

    • 1: By definition, a composite number must be greater than 1.
    • 8.4: It is a decimal number.
    • 13: It is a prime number (divisible only by 1 and 13).
    • $\mathbf{\dfrac{9}{2}}$: It is a fraction, not a whole number.
  3. List all prime numbers between 30 and 50 inclusive.
    View Solution

    The prime numbers between 30 and 50 are:
    31, 37, 41, 43, 47

  4. List all composite numbers between 100 and 110 inclusive.
    View Solution

    The composite numbers between 100 and 110 inclusive are:
    100, 102, 104, 105, 106, 108, 110

    (Note: 101, 103, 107, and 109 are prime numbers).

  5. Is the sum of two prime numbers always a prime number?
    View Solution

    No. Here is an example that proves this false:

    3 + 7 = 10

    Both 3 and 7 are prime numbers, but their sum (10) is a composite number.

  6. Is the product of two prime numbers also a prime number?
    View Solution

    Never. The resulting product will always have at least four factors: 1, itself, and the two original prime numbers.

    Example: 7 × 11 = 77. The number 77 has the factors 1, 7, 11, and 77, making it a composite number.

  7. Which is the largest 3-digit prime number?
    View Solution

    Start checking downwards from the largest 3-digit number (999):

    • 999 is divisible by 3 and 9 (Not prime).
    • 998 is an even number divisible by 2 (Not prime).
    • 997 cannot be divided evenly by any prime number up to its square root (~31.5).

    Answer: 997 is the largest 3-digit prime number.

  8. Which is the smallest 2-digit prime number?
    View Solution

    Start checking upwards from the smallest 2-digit number (10):

    • 10 is divisible by 2 and 5 (Not prime).
    • 11 is only divisible by 1 and itself.

    Answer: 11 is the smallest 2-digit prime number.

  9. List all the two-digit prime numbers that can be made from the digits 1, 3 and 6 (using each digit only once per number).
    View Solution

    First, list all possible two-digit combinations: 13, 16, 31, 36, 61, 63.

    Next, eliminate the composite numbers:

    • 16 and 36 are even (divisible by 2).
    • 63 is divisible by 3 and 9.

    The remaining prime numbers are: 13, 31, and 61.

  10. Can you find a prime number whose least significant digit (the digit on the far right) is 0?
    View Solution

    No. Any whole number ending in 0 is divisible by 2, 5, and 10. Therefore, it will always be a composite number (or 0 itself, which is neither prime nor composite).

  11. Can you find a multi-digit prime number whose least significant digit (the digit on the far right) is 5?
    View Solution

    No. The only prime number ending in 5 is the number 5 itself. Any multi-digit number ending in 5 (such as 15, 25, 35...) is guaranteed to be evenly divisible by 5, making it a composite number.

  12. Can you find a prime number such that the sum of all its digits is equal to 12?
    View Solution

    No. There is a mathematical divisibility rule stating that if the sum of a number's digits is divisible by 3, the entire number is divisible by 3. Since 12 is divisible by 3, any number whose digits add up to 12 will also be divisible by 3, making it a composite number.

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