Multiples, factors, primes and squares

📌 Key points

1. Multiples of 6 are in the 6 times table: 6, 12, 18, 24, … Multiples go on for ever.
2. A factor divides exactly into a number. The factors of 12 are 1, 2, 3, 4, 6 and 12.
3. Factors come in pairs that multiply to make the number: 18 = 1 × 18 = 2 × 9 = 3 × 6.
4. A prime number has exactly two factors, 1 and itself. The primes below 30 are 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29.
5. 1 is not a prime number because it has only one factor. 2 is the only even prime number.
6. A square number is a whole number times itself: 7² = 7 × 7 = 49. A cube number is n × n × n: 2³ = 2 × 2 × 2 = 8.
7. A number divides by 3 if its digit sum divides by 3, and by 9 if its digit sum divides by 9.
8. A number divides by 4 if its last two digits divide by 4; it divides by 5 if it ends in 0 or 5.
9. A common multiple is in both times tables (12 is a common multiple of 3 and 4). A common factor divides into both numbers.

📖 Key words

Multiple

The answer when you multiply a number by a whole number, e.g. 35 is a multiple of 7.

Factor

A whole number that divides exactly into another number.

Prime number

A number with exactly two factors: 1 and itself.

Square number

A whole number multiplied by itself, e.g. 25 = 5 × 5.

Cube number

A whole number multiplied by itself three times, e.g. 27 = 3 × 3 × 3.

Common multiple

A number that is a multiple of two or more numbers.

Common factor

A number that is a factor of two or more numbers.