Card 1 of 8
Number facts
Primes, squares, cubes, Fibonacci, triangular numbers and the divisibility rules.
Prime numbers under 100
There are 25 of them:
2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97
The rules that catch children out:
- 1 is NOT prime (a prime has exactly two factors; 1 has one).
- 2 is prime — and it's the only even prime.
- A prime has exactly two factors: 1 and itself.
The fake primes. These look prime and are the examiner's favourite trap:
| Looks prime | Actually | How to spot it |
|---|---|---|
| 51 | 3 × 17 | digits 5+1=6, divisible by 3 |
| 57 | 3 × 19 | digits 5+7=12, divisible by 3 |
| 87 | 3 × 29 | digits 8+7=15, divisible by 3 |
| 91 | 7 × 13 | no digit trick — just memorise it |
| 119 | 7 × 17 | no digit trick — just memorise it |
Square numbers (know to 15²)
| n | n² |
|---|---|
| 1 | 1 |
| 2 | 4 |
| 3 | 9 |
| 4 | 16 |
| 5 | 25 |
| 6 | 36 |
| 7 | 49 |
| 8 | 64 |
| 9 | 81 |
| 10 | 100 |
| 11 | 121 |
| 12 | 144 |
| 13 | 169 |
| 14 | 196 |
| 15 | 225 |
Cube numbers (know to 10³)
| n | n³ |
|---|---|
| 1 | 1 |
| 2 | 8 |
| 3 | 27 |
| 4 | 64 |
| 5 | 125 |
| 6 | 216 |
| 7 | 343 |
| 8 | 512 |
| 9 | 729 |
| 10 | 1000 |
Fibonacci sequence
Each term is the sum of the previous two:
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, …
Start 1, 1. Then 1+1=2, 1+2=3, 2+3=5, 3+5=8. If a sequence's third term equals its first two added, test Fibonacci.
Triangular numbers
1, 3, 6, 10, 15, 21, 28, 36, 45, 55, …
Differences go up by one each time (+2, +3, +4, +5…). They're the dot-triangle numbers: 1 dot, then 3, then 6.
Divisibility tests
| Divisible by | Test |
|---|---|
| 2 | Last digit is even |
| 3 | Digit sum divisible by 3 |
| 4 | Last two digits divisible by 4 |
| 5 | Ends in 0 or 5 |
| 6 | Passes the 2-test and the 3-test |
| 8 | Last three digits divisible by 8 |
| 9 | Digit sum divisible by 9 |
| 10 | Ends in 0 |
| 11 | Alternating digit sum (add, subtract, add…) gives 0 or a multiple of 11 |