Special Types of Number

Understanding Special Types of Numbers

  • Special numbers refer to those that have some interesting or unique characteristics in mathematics. Understanding these types of numbers and their properties is critical in navigating more advanced mathematical concepts.

Prime Numbers

  • A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. In other words, if a number is prime, it cannot be formed by multiplying two smaller natural numbers.
  • For instance, the prime numbers less than twenty are 2, 3, 5, 7, 11, 13, 17 and 19.
  • As an exception, ‘1’ is not considered a prime number.

Composite Numbers

  • A composite number is a positive number that has at least one positive divisor other than one or itself. In other words, it can be formed by multiplying two smaller numbers.
  • For example, the composite numbers less than ten are 4, 6, 8 and 9.
  • Note that all non-prime natural numbers are composite numbers.

Square Numbers

  • A square number is the result when a number has been multiplied by itself.
  • For instance, here are the first five square numbers: 1 (1x1), 4 (2x2), 9 (3x3), 16 (4x4), 25 (5x5).
  • A square number can never be negative because any number multiplied by itself results in a positive product.

Cube Numbers

  • A cube number is the outcome when a particular number is multiplied by itself twice. Essentially, if the volume of a cube is given by side^3, and all sides are equal, then that number is a cube number.
  • Here are the first five cube numbers: 1 (1x1x1), 8 (2x2x2), 27 (3x3x3), 64 (4x4x4) and 125 (5x5x5).

Practice Problems

  • Problem: Find the first five prime numbers greater than 20.
    • Solution: 23, 29, 31, 37, 41
  • Problem: Identify if the number 63 is a composite number.
    • Solution: Yes, 63 is a composite number with factors 1,3,7,9,21 and 63.
  • Problem: What is the square of 9?
    • Solution: 81 (9x9 = 81)
  • Problem: What is the cube of 4?
    • Solution: 64 (4x4x4 = 64)

Key Takeaways

  • Be proficient in identifying prime, composite, square, and cube numbers.
  • Comprehend that while all prime numbers are also composite numbers, not all composite numbers are prime.
  • It is important to understand that square and cube numbers refer to the number of times a number is multiplied by itself.
  • Continue working on exercises to get more comfortable with these distinctive number types. Practice will help you spot these number types more quickly and easily.