How to factor

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In this post we are going to learn how to factor into prime numbers.

First, let’s look at what factoring is: writing a number as the multiplication of other numbers.

For example, let’s factor the number 12.

12 = 3 x 4

12 = 2 x 6

12 = 1 x 12

All 3 cases are examples of factoring.

Now we are going to look at what a prime number is: those numbers that are only divisible by themselves and 1.

For example, 5 is a prime number because it is only divisible by 5 and 1. But 6 is not a prime number because it is divisible by 1, 2, 3, and 6.

Prime numbers table up to 100factor

Now you know what factoring is and what prime number are!

Factoring into prime numbers is writing any number as the multiplication of prime numbers.

For Example, we are going to factor the number 36.

Let’s choose a prime number by which 36 is divisible, for example 2.

36 ÷ 2 = 18

Now we divide 18 by another prime number.

18 ÷ 2 = 9

Now we divide 9

9 ÷ 3 = 3

And finally we divide the 3, which is a prime number, so we can only divide it by itself.

3 ÷ 3 = 1

So 36, when factored into prime factors looks like this: 2 x 2 x 3 x 3

We can also write the factors in the form of powers, so that the 2 is multiplied twice and the 3 is multiplied twice: 36 = 2 2 x 3 2

If you want to learn more about prime numbers and factoring, check the posts below:

  • Prime Numbers
  • More About Prime Numbers
  • Factorization

To keep learning, you can sign up at Smartick and learn more math every day!

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Learn More:

  • Review Factoring with Examples
  • Factorization: What Is It and How Is It Done?
  • Prime Numbers: Activities with Smartick
  • Follow 8 Easy Steps to Factor a Number
  • Prime Numbers and Composite Numbers

Weather Dynamics

At the first glance the dynamics of how weather affects demand might appear complex. There are numerous components like temperature and sunshine, as well as factors like day-of-the-week, time-of-the-year, geography, type of product … However, it does not have to be overly complex. To simplify things; weather has two distinct kinds of effects on consumer behaviour.

  • People are more likely to go out more on a beautiful day, increasing the overall traffic and sales at the store level.
  • Consumer buying patterns being affected by weather, different products and product groups have different responses to weather changes.

Let’s discuss these two effects briefly. The impact of weather on overall traffic is most obvious during the summer with winter weather generally having far less impact (even in freezing Finland). A beautiful summer day can easily boost shop traffic by 5-10% compared to the seasonal average with weather factored out, while a cold rainy day has the opposite effect and reduces it. However the degree to which demand responds to the weather can differ considerably according to location and also market type. For example larger stores tend to feel the impact of a warm weekend more than smaller ones as people go to stock up for the weekend’s big barbecue party.

There’s also an enormous variation in the response to weather across different products and product groups. However, some factors remain more or less universal. The impact of good or bad weather is often asymmetric, as in the ice cream example above, because the potential sales increase as a result of good weather is stronger than the negative impact of bad weather. An example of weather impact is illustrated below. While there is quite a lot of noise in data, distinct significant impacts can be observed for the two largest heat waves.

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Screenshot 2014-10-14 15.04.37Figure 1. Example of weather impact. Sales of all fresh products, ice creams and beverages (hence including most weather hot-weather sensitive products) for one store in June-July

However, both of the effects of the weather mentioned above have a zero-sum counter-part. Firstly, while people are more likely to go out to do their shopping on a beautiful day, conversely that means they will have, to some extent stocked up for other (perhaps less beautiful) days. So it’s apparent that the weather in part only shifts demand rather than just decreasing or increasing it. Secondly when sales of products that respond positively to hot-weather go up, people tend to spend slightly less on other products.

As well as the points made above, there are a number of subtle variations to the dynamics of how weather affects consumer behaviour. For instance responses to the weather may differ depending on the day of the week; prolonged good weather often desensitises consumers – the more beautiful days there are, the less people feel the need to make an event of them when they appear. However, the impact of such factors is of lesser significance. For instance, when separating out normal weekday variation from demand, the sales response to weather is typically reasonably uniform throughout the week.

So let’s next look at simple steps that you can take in order to start improving your forecast quality by taking the weather into account.

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