## Prime Factorisation with Multiplication and Division

Use multiplication and division with primes and prime factorisation to defeat the alien invasions. Make use of divisibility strategies to achieve higher scores and progress to the next challenge.

### Instructions

#### Game Goals

In this maths game your goal is to protect the remote moonbase Sigma Prime from marauding alien invaders.

The game tests your skill at splitting numbers into the product of their prime factors. By firing prime numbers at the aliens you must reduce their values to 1 and destroy them!

The alien assault is merciless and relentless – how long can you survive?

#### How To Play

The alien invaders appear randomly at the top of the play area and home in on Sigma Prime.

Each alien displays a number value – by firing prime number missiles at the alien, your aim is to divide its value down to 1 and so destroy it! But take care, you must only hit an alien with its prime factors.

If an alien makes it through your defences or you hit an alien with a prime that is not a factor, ‘Remainder Rubble’ will rain down.

As Remainder Rubble accumulates at the bottom of the screen, it pushes Sigma Prime closer and closer to the lethal Laser Wire at the top of the screen – one touch of this deadly barrier spells disaster, and ends the game!

Stay alert for surprise appearances by alien Motherships. These giant vessels glide across the top of the play area and are worth big points if you manage to bring them down!

The aliens attack in waves. As the waves progress, the aliens become faster and tougher to destroy. Fortunately, after each wave, any Remainder Rubble is cleared from play so you always start a new wave back on the ground.

Sigma Prime features 24 unique attack waves. Before a game begins, you have the option to start play from any wave reached previously – though note that skipping the earlier waves will reduce your score and make medals harder to earn! If you beat all 24 waves, the game will ‘loop’ back to the start – but now with the aliens faster than before!

#### Game Controls

Guide the target crosshair with your mouse. Launch a prime number missile by pressing the appropriate arrow key on your keyboard.

If the game is in Window mode, you can also use the A, W and D keys to launch primes.

The primes available and their corresponding arrow keys are shown in the display at the bottom-right of the play area. The primes change from wave to wave – sometimes you even have three primes to launch! – so be sure to check this display each time a new wave starts.

When you destroy an alien with a value consisting of two or more prime numbers, the corresponding factor tree appears in the ‘Analysis’ column on the right of the play area so you can see exactly how you brought the alien down!

#### Scoring

The scoring increases as you progress from one wave to next:

- Points per correct hit
- 25× wave number
- Points per alien destroyed
- 50× wave number
- Points per Mothership destroyed
- 1,000× wave number

At the end of each wave, you receive a bonus. The bonus is proportional to how far Sigma Prime has been pushed up the screen by Remainder Rubble, and is also multiplied by the wave number.

**'End of wave' bonus points**

*= 1000 × (percentage distance from Laser Wire) × (wave number)*So, if Sigma Prime ends a wave at ground level (i.e. it has not been pushed up the screen at all), you get the full bonus. However, if Sigma Prime ends a wave pushed halfway up the screen, you get half the bonus. And if Sigma Prime ends a wave almost touching the Laser Wire, you get next to no bonus at all!

### Improve your score

#### Basic Strategies

- When a new wave starts, familarise yourself with which primes correspond to which buttons as quickly as possible.
- Try to destroy aliens as quickly as you can after they appear – if you let the alien hordes build up, you can get overwhelmed quickly.
- Remember: you don’t need to destroy the Motherships to complete a wave. Although they’re worth big points, if you’re struggling it’s better to focus on the aliens.
- Learn basic divisibility tricks to get in some early hits, reducing your alien enemies to more manageable quantities.
- When an alien appears, if its number is small enough then try to work out all of its prime factors and destroy it with a quick salvo of shots. For example, if an alien appears with 25 on it then fire off two 5s in quick succession – this will destroy it because 25 = 5 × 5.
- Similarly, learn standard finishes – for example, 2, 2, 3 will finish off a 12 because 2 × 2 × 3 = 12
- Aliens attack at different speeds so take this into account when deciding which ones to target and exactly when to fire.

#### Maths Strategies

- Even numbers end in 0, 2, 4, 6 or 8. They are divisible by 2.
- Numbers that end in 0 or 5 have 5 as a prime factor.
- If a number ends in 0 then its divisible by 10 so hit it with a 2, 5 salvo.
- If a numbers ends in 00 then its divisible by 100 so hit it with a 2, 5, 2, 5 salvo.
- If the sum of the digits of a number is a multiple of 3 then the number itself is divisible by 3.
- If the sum of the digits of a number is divisible by 9 then the number itself is divisible by 9.
- Learn the squares of the prime numbers in the game: 2² = 4, 3² = 9, 5² = 25
- Learn the cubes of some of the prime numbers: 2³ = 8, 3³ = 27, 5³ = 125
- Any number in this sequence can be destroyed by 2s only: 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096,…
- And any number in this sequence can be destroyed by 3s only: 3, 9, 27, 81, 243, 729,…