Sheet 1 of 10 · Maths

Number facts

Squares, cubes, primes, divisibility, factors and rounding. 9 rules, each with a worked example.

Squares, cubes and primes

Square numbers
n² equals n × n
- 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225 (1² to 15²)
Example12² = 12 × 12 = 144
Cube numbers
n³ equals n × n × n
- 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000 (1³ to 10³)
Example4³ = 4 × 4 × 4 = 64
Tip: 64 is both a square (8²) and a cube (4³).
Prime numbers under 100
A prime has exactly two factors: 1 and itself
- 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 (25 primes in all)
Tip: 1 is not prime. 2 is the only even prime.

By 2, 4, 5, 8 and 10
Look at the last digits
- 2: last digit is even · 5: ends in 0 or 5 · 10: ends in 0
- 4: last two digits divide by 4 · 8: last three digits divide by 8
Example3,716: 16 ÷ 4 = 4, so 3,716 divides by 4 (3,716 ÷ 4 = 929)
By 3, 6 and 9
Add up the digits
- 3: digit total divides by 3 · 9: digit total divides by 9
- 6: the number is even AND divides by 3
Example738: 7 + 3 + 8 = 18, so 738 divides by 3, 6 and 9

Factors vs multiples
Factors go INTO a number; multiples are in its times table
ExampleFactors of 12: 1, 2, 3, 4, 6, 12 · Multiples of 12: 12, 24, 36, 48…
Tip: Factors are few, multiples go on for ever.
HCF and LCM
HCF = highest common factor · LCM = lowest common multiple
- HCF: list the factors of both and pick the biggest one they share
- LCM: list the multiples of both and pick the smallest one they share
Example12 and 18: HCF = 6, LCM = 36

Place value
Th H T O . tenths hundredths
ExampleIn 34.57 the 5 is 5 tenths (0.5) and the 7 is 7 hundredths (0.07)
Tip: × 10 moves every digit one place left; ÷ 10 moves it one place right.
Rounding
Look at the next digit: 5 or more, round up; 4 or less, round down
Example3,465 to the nearest 100 = 3,500 · 7.348 to 1 decimal place = 7.3

The study guide goes through each rule step by step, with more examples.