Prime Factorisation As a Technique For Efficient Problem Solving

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Prime factorisation simply means to express a number as a product of its prime factors For example, the prime factors of the number 12 are; 2x2x3. Notice that all the factors are prime factors that is number that can only be divided by 1 and itself.

Most kids encounter prime factorisation in accelerated math programmes around 4th-5th grade.

Knowing this technique allows us to work on certain questions which requires us to find the prime factors or roots of certain large numbers.

On a softer note, you can use the skills learnt in prime factorisation to help you identify the component parts of a large project.

I will provide you with two examples of questions in which prime factorisation will come in handy.

Example A: Divide these four numbers, 15,33,35 and 77 into two groups so that the product of the numbers in each group are equal.

This question might stump some people. However, i you are able to apply the technique of prime factorisation and break all the four numbers into its prime factors you can easily get the answer.

Solution: 15= 3×5, 33=3×11, 35=5×7,77=7×11.

Looking the prime factors of all the four numbers, you can tell that 33 is not going to be in the same group as 77 since each group must contain the number ’11’ at least once.

Thus the two number are, Group 1: 15 & 77. Group 2: 33 & 35. Group 1: 15×77=3x5x7x11. Group 2: 3x5x7x11.

Example B: Find three consecutive even numbers whose product is 13728.

Applying prime factorisation gives us

13728=2x2x2x2x2x3x11x13

= 2x2x2x11x12x13

Thus, the three even numbers are 22, 24 & 26.

This is the beauty of prime factorisation It allows you to break down large numbers into its prime factors and easily identify the factors.

Besides learning how to break the number into its component parts or prime factors you can also transfer the skills you have learnt in prime factorisation to managing major assignments. For instance, you can use this technique to identify the ‘root’ or critical factors of a big project. This enables you to plan the project more carefully as you can see how the individual parts fit together.

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Source by Penny Chow