Real Numbers

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Every composite number can be expressed (factorised) as a product of primes, and this factorisation is unique, apart from the order in which the prime factors occur. For example: 12 = 2² × 3 (this is

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It means that for any composite number, there is one and only one way to write it as a product of primes (ignoring the order). For example, 30 can only be written as 2 × 3 × 5, regardless of the order

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32760 = 2³ × 3² × 5 × 7 × 13. This is found by factorising: 32760 = 2 × 2 × 2 × 3 × 3 × 5 × 7 × 13 = 2³ × 3² × 5¹ × 7¹ × 13¹

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A composite number is a natural number greater than 1 that has at least one positive divisor other than 1 and itself. In other words, it can be expressed as a product of smaller natural numbers. Examp

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A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. Examples: 2, 3, 5, 7, 11, 13, 17, 19, 23, etc. Note: 1 is neither prime nor composite.

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Let p be a prime number. If p divides a², then p divides a, where a is a positive integer. This theorem is crucial for proving the irrationality of square roots.

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An irrational number is a number that cannot be written in the form p/q, where p and q are integers and q ≠ 0. Examples include √2, √3, √5, π, etc. These numbers have non-terminating, non-repeating de

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A rational number is a number that can be written in the form p/q, where p and q are integers and q ≠ 0. Examples: 1/2, 3/4, -2/5, 7 (which is 7/1), 0.5 (which is 1/2), etc.