Higher November 2024 Paper 6 Q8
8
(a) 198 and 495 are written below as the product of their prime factors.
\(198 = 2 \times 3^2 \times 11 \qquad 495 = 3^2 \times 5 \times 11\)
Work out the highest common factor (HCF) of 198 and 495. [2]
(b) A five-digit passcode is created using the lowest common multiple (LCM) followed by the highest common factor (HCF) of two numbers.
The two numbers chosen are 198 and 495.
The two numbers chosen are 198 and 495.
(i) To try and find the passcode, a computer hacker multiplies the highest common factor (HCF) of 198 and 495 by 5 and uses this as the lowest common multiple (LCM) in the passcode.
The computer hacker’s passcode is incorrect.
Write down the omission in the computer hacker’s method. [1]
The computer hacker’s passcode is incorrect.
Write down the omission in the computer hacker’s method. [1]
(ii) Work out the correct five-digit passcode. [2]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 99 | 2 | M1 for identification of 3 (or 32 or 9) and 11 as common factors, not spoilt | Venn diagram on its own scores 0 unless 32 and 11 selected |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| (i) They did not multiply by 2 oe | 1 | See appendix | |
| (ii) 99099 | 2 | B1 for [LCM] 990 soi by passcode or M1 for 2 × 32 × 5 × 11 oe | FT their (a) eg (a) 46 (b) 2 marks for 99099, 99046, 46046 or B1 for (a) × 10 |
Appendix: Exemplar responses for Q8(b)(i)
An acceptable response will usually refer to 2
| Response | Mark |
|---|---|
| They did not multiply by 2 / they should have multiplied by 2 | 1 |
| They have forgotten 2 (implies omission) | BOD 1 |
| They needed to multiply by 10 instead of 5 (this is not the omission) | 0 |
| 99 x 5 x 2 (doesn’t identify the omission) | 0 |
| 990 | 0 |
| He should multiply by 2 not by 5 | 0 |