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 kids encounter prime factorization in accelerated math programs around 4th and 5th grade.
Knowing this technique allows us to work on certain questions that force 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 component parts of a large project.
I will provide you with two sample 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 the same.
This question might puzzle some people. However, if you can apply the prime factorization technique and decompose 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 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 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.
Applying prime factorization gives us
13728=2x2x2x2x2x3x11x13
= 2x2x2x11x12x13
Therefore, the three even numbers are 22, 24, and 26.
This is the beauty of prime factorization. It allows you to break down large numbers into their prime factors and easily identify the factors.
In addition to learning how to break down the number into its component parts, or prime factors, you can also transfer the skills you’ve learned in prime factorization to managing important 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 pieces fit together.