Number Properties
Explore factors, multiples, prime numbers, and learn to find the Highest Common Factor and Lowest Common Multiple.
Factors & Multiples
Factors
A factor of a number divides into it exactly (with no remainder). Every number has at least two factors: 1 and itself.
Factors of 24:
Find pairs: 1×24, 2×12, 3×8, 4×6
Multiples
A multiple of a number is the result of multiplying it by a whole number (1, 2, 3, ...). Multiples go on forever.
First 6 multiples of 7:
7×1, 7×2, 7×3, 7×4, 7×5, 7×6
Prime & Composite Numbers
Prime Numbers
A prime number has exactly two factors: 1 and itself. It cannot be divided evenly by any other number.
Primes up to 30: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29
Note: 1 is NOT prime (only one factor). 2 is the only even prime.
Composite Numbers
A composite number has more than two factors — it can be divided by numbers other than 1 and itself.
Examples: 4 (factors: 1, 2, 4), 15 (factors: 1, 3, 5, 15), 36
Every composite number can be written as a product of primes.
Highest Common Factor (HCF) & Lowest Common Multiple (LCM)
HCF — Highest Common Factor
The largest factor that is shared by two or more numbers. Used to simplify fractions.
Find HCF of 12 and 18:
Factors of 12: {1, 2, 3, 4, 6, 12}
Factors of 18: {1, 2, 3, 6, 9, 18}
HCF = 6
LCM — Lowest Common Multiple
The smallest multiple shared by two or more numbers. Used when adding fractions.
Find LCM of 4 and 6:
Multiples of 4: 4, 8, 12, 16, 20, 24...
Multiples of 6: 6, 12, 18, 24...
LCM = 12
Key Vocabulary
Factor
A whole number that divides exactly into another number. All factors of 12: 1, 2, 3, 4, 6, 12.
Multiple
The result of multiplying a number by a positive integer. Multiples of 5: 5, 10, 15, 20, ...
Prime Number
A number with exactly two factors — 1 and itself. Examples: 2, 3, 5, 7, 11, 13.
Prime Factorisation
Writing a number as a product of prime numbers. E.g. 12 = 2 × 2 × 3 = 2² × 3.
Worked Examples
List all factors of 36.
Find pairs that multiply to 36:
1 × 36, 2 × 18, 3 × 12, 4 × 9, 6 × 6
Factors: {1, 2, 3, 4, 6, 9, 12, 18, 36}
Find the HCF of 20 and 30.
Factors of 20: {1, 2, 4, 5, 10, 20}
Factors of 30: {1, 2, 3, 5, 6, 10, 15, 30}
Common factors: {1, 2, 5, 10}
HCF = 10
Find the LCM of 8 and 10.
Multiples of 8: 8, 16, 24, 32, 40, 48...
Multiples of 10: 10, 20, 30, 40, 50...
First common multiple: 40
LCM = 40
Knowledge Check
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Key Concepts Summary
- ●Factors divide a number exactly; find them in pairs working outward from 1.
- ●Multiples are the times table of a number (infinite); a multiple is always larger than or equal to the number.
- ●Prime numbers have exactly two factors (1 and themselves). 1 is not prime.
- ●The HCF is the largest factor common to two numbers — useful for simplifying fractions.
- ●The LCM is the smallest multiple shared by two numbers — useful for finding the LCD when adding fractions.