Prime Factorisation

Understanding Prime Factorisation

  • Prime Factorisation is the process of breaking down a number into its basic building blocks, which are all prime numbers.
  • A prime number is a number that has only two factors: 1 and itself. The first few prime numbers are 2, 3, 5, 7, 11 and 13.
  • In prime factorisation, every composite (non-prime) number can be distinctly factorised into prime numbers and this representation is unique except for the order of the factors.

Process of Prime Factorisation

  • Identify a prime number that can divide the given number. Remember that 2 is a prime number and can divide all even numbers.
  • Divide the number and write down the quotient and the prime factor.
  • Repeat the process with the quotient until you are left with a quotient that is a prime number. Then, write down your final prime factor.

Prime Factorisation and Exponents

  • When you get a list of prime factors after completing the prime factorisation, you might notice some of these factors are repeated.
  • In that case, you can use exponents to simplify the representation. For example, if you factorise 180, the factors are 2, 2, 3, 3, and 5. You can write this as 2², 3², 5.
  • The exponent indicates how many times that prime number divides into the original number.

Applications of Prime Factorisation

  • Prime factorisation is used in many branches of mathematics, including algebra, number theory and also in understanding concepts like greatest common factor (GCF) and least common multiple (LCM).
  • It is also used in computer science and cryptography, for example in the RSA encryption system, which is widely used for secure data transmission.

Common Mistakes to Avoid

  • Not continuing the division until only prime numbers are left. Every composite (non-prime) number should be divided further until only prime numbers remain.
  • Forgetting to use exponents when prime factors are repeated. This makes your factorisation representation neat and clear.
  • Mistaking 1 as a prime number. Remember that 1 is not a prime number since it only has one factor: itself.
  • Misidentifying prime numbers. Make sure you memorize at least the first few prime numbers to aid in the factorisation process.