Your learning journey
Find and justify factors, prime factorisations, HCFs and LCMs; choose the right structure for a problem.
Work without a calculator except for an invited check. Keyboard - means the same as −. Attempt before opening a scaffold or intentional practice explanation.
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Ready.
Connect & Check
Factor: divides a whole number exactly. Multiple: an integer times a number. Prime: integer greater than 1 with exactly two positive factors. HCF: highest common factor. LCM: lowest common multiple.
Intentional practice feedback after your attempt
42; 7.
Division reverses multiplication.
Intentional practice feedback after your attempt
3 × 3 = 9.
The index counts equal factors.
Intentional practice feedback after your attempt
2 and 11.
9 also has factor 3.
Present
Factors come in pairs: 18 = 1 × 18 = 2 × 9 = 3 × 6. After pairs cross, no new factors appear. A prime factorisation splits until every factor is prime; 18 = 2 × 3 × 3. Different valid splits give the same prime factors.
List factors in pairs. For HCF select prime factors shared by both numbers, with the smaller powers. For LCM include every prime needed, with the larger powers. Check that HCF divides both and LCM is divisible by both.
Optional scaffold
Stop when factor pairs start repeating.
Intentional practice feedback after your attempt
1, 2, 4, 5, 10, 20.
Pair 1×20, 2×10 and 4×5.
Optional scaffold
Split 6 into 2 × 3.
Intentional practice feedback after your attempt
2³ × 3.
All final factors must be prime.
Optional scaffold
Use the smaller powers for common factors.
Intentional practice feedback after your attempt
6.
Both contain one 2 and one 3.
Optional scaffold
Check 24 ÷ 8 and 24 ÷ 12.
Intentional practice feedback after your attempt
24.
2³ × 3 contains every required prime factor.
Apply
Optional scaffold
List factors and multiples in separate columns.
Intentional practice feedback after your attempt
3 and 18; 6 and 12.
When one number divides the other, it is the HCF and the larger is the LCM.
Intentional practice feedback after your attempt
30=2×3×5; 45=3²×5; HCF 15; LCM 90.
Use smaller powers for HCF and larger for LCM.
Optional scaffold
List positive common multiples.
Intentional practice feedback after your attempt
36 seconds.
A shared time must be a multiple of both periods.
Optional check after A2: 90 ÷ 30 = 3 and 90 ÷ 45 = 2. A calculator checks divisibility but does not establish that a multiple is the lowest.
Apply and extend
Intentional practice feedback after your attempt
Yes. Their only shared positive factor is 1.
A common factor greater than 1 would have to equal both primes.
Optional scaffold
Write 12=2²×3 and 18=2×3².
Intentional practice feedback after your attempt
6×36=216=12×18.
For each prime, the smaller and larger exponents together preserve both original exponents.
Access, Scaffold, Core and Stretch support the same goal. Stretch deepens reasoning for either qualification tier.
Recall & Review
Retrieval without notes
Six retrieval points. Enter a number, decimal, fraction such as 3/2, or mixed number such as 1 1/2. Equivalent numeric values are accepted. Unsupported notation goes to teacher review. For rounding, also communicate the requested accuracy in written work; numerical scoring cannot judge significant trailing zeros.
Not checked.
Independent exit evidence
P1–P2: five minutes, no notes, 4 marks. Your teacher reviews working and explanations. Full assessment solutions are not embedded.
Recall & Review and prepare
Multiplying or dividing the top and bottom of a fraction by the same non-zero number preserves its value. The whole stays fixed. We will use common factors to simplify.
Retrieve F1 again in one week. Bring your working and one question.
Your progress summary
Completion records attempts, not mastery. Retrieval points describe the latest checked attempt. Your teacher reviews P1–P2 separately and checks retained understanding after a delay.
Restore a backup
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Optional extension activities
Stretch
Check after attempting
84=2²×3×7; 126=2×3²×7; HCF=42, LCM=252.
Deep challenge
Check after attempting
Product of numbers=HCF×LCM=1080; other=1080/30=36.