Prime Time

Factors and multiples, prime and composite numbers, divisibility tests, prime factorisation, and the HCF and LCM.

Key ideas

• A factor divides a number exactly; a multiple is the number times 1, 2, 3, …
• A prime has exactly two factors, 1 and itself. 1 is neither prime nor composite; 2 is the only even prime.
• Co-prime numbers have no common factor other than 1, such as 8 and 15.
• Divisible by 2: last digit even. By 3 or 9: digit sum divisible by 3 or 9. By 5: ends in 0 or 5. By 10: ends in 0.
• Divisible by 4: last two digits divisible by 4. By 8: last three digits divisible by 8.
• The HCF (largest common factor) solves “largest equal piece or tile”; the LCM (smallest common multiple) solves “when do they meet again”.

Remember

Watch out

• Calling 1 a prime number.
• Mixing up factors (fewer, smaller) and multiples (endless, larger).
• Using the LCM for a tiling problem (it needs the HCF).

Worked example