Middle school maths, year 1 · unit 1
Prime Factorisation
Split matter and you reach atoms; split a number and you reach numbers that cannot be split any further. Know those, and sharing things out or matching up times stops being sums and becomes something you can see. Start by sharing out candies.
Some numbers cannot be split any further
A board to arrange12 is 2×6 and 6 is 2×3, but 2 and 3 will not split. Drag a prime marble onto a number block.
When do the two buses leave together?
A board to adjustOne bus leaves every 4 minutes, the other every 6. Drag the gold handle to let time pass.
Try it yourself
Use what you found on the boards. The numbers change every time and the easy questions come first. Get three right and the lamp lights.
What to take away from this unit
- A number that divides another exactly is a divisor of it. Divisors come in pairs: 12 = 1×12 = 2×6 = 3×4.
- A number divisible only by 1 and itself is a prime (2, 3, 5, 7, 11, …). 1 is not prime. A number of 2 or more that is not prime is a composite number.
- Writing a number as a product of primes is prime factorisation. A number multiplied by itself several times is shortened to a power: 60 = 2×2×3×5 = 2²×3×5. Whatever order you split in, there is only one result.
- The largest number dividing both is the greatest common divisor; the first number that is a multiple of both is the least common multiple. Once both are factorised, each can be seen at a glance.