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## Prime Factorisation As a Technique For Efficient Problem Solving

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

Most children encounter prime factorization in accelerated math programs around 4th-5th grade.

Knowing this technique allows us to work on certain issues that require us to find the prime factors or roots of certain large numbers.

On a lighter note, you can use the skills learned in prime factorization to help you identify the components of a large project.

I’ll give you two examples of questions where prime factorization 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 is equal.

This question may surprise some people. However, if you can apply the technique of prime factorization and divide the four numbers into their prime factors, you can easily get the answer.

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

Looking at the prime factors of the four numbers, you can tell that 33 will not be in the same group as 77, since each group must contain the number “11” at least once.

So the two numbers are, Group 1: 15 and 77. Group 2: 33 and 35. Group 1: 15×77=3x5x7x11. Group 2: 3x5x7x11.

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

The application of prime factorization gives us

13728=2x2x2x2x2x3x11x13

= 2x2x2x11x12x13

So the three even numbers are 22, 24 and 26.

This is the beauty of prime factorization. It allows you to decompose large numbers into their prime factors and identify them easily.

In addition to learning how to divide a number into its component parts or prime factors, you can also transfer the skills you’ve learned in prime factorization to managing major tasks. For example, you can use this technique to identify the “root” or critical factors of a large project. This allows you to plan the project more carefully as you can see how the individual parts fit together.

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