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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, that is, a number that can only be divided by 1 and itself.
Most children encounter prime factorization in accelerated math programs around 4th and 5th grade.
Knowing this technique allows us to work on certain questions that require us to find the prime factors or roots of certain large numbers.
On a softer note, you can use the skills learned in prime factoring to help you identify the components of a large project.
I’ll give you two examples of questions where prime factorization will be useful.
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 might confuse some people. However, if you are able to apply the prime factoring technique and factorize the four numbers into prime factors, you can easily get the answer.
Solution: 15= 3×5, 33=3×11, 35=5×7,77=7×11.
By 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 & 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 the prime factorization gives us
So the three even numbers are 22, 24 and 26.
That’s the beauty of prime factorization. It allows you to decompose large numbers into prime factors and easily identify the factors.
In addition to learning how to decompose the number into its components or prime factors, you can also transfer the skills you learned in prime factorization to handling major assignments. 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 because you can see how the different pieces fit together.
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