AS June 2018 Q1
1.
(i) Using a suitable algorithm and without performing any division, determine whether 23 738 is divisible by 11 (2)
(ii) Use the Euclidean algorithm to find the highest common factor of 2322 and 654 (3)
| Scheme | Marks | AO |
|---|---|---|
| \(2 - 3 + 7 - 3 + 8 = \ldots\) or \(2 + 7 + 8 - (3 + 3) = \ldots\) | M1 | 1.1b |
| \(= 11\) so 23 738 is divisible by 11 | A1 | 1.1b |
| (2) |
Notes
M1: Executes the correct process by adding and subtracting alternating digits or equivalent
A1: Completes correctly with a correct conclusion
| Scheme | Marks | AO |
|---|---|---|
| \(2322 = 3 \times 654 + 360, \quad 654 = 1 \times 360 + 294\) | M1 | 1.2 |
| \(360 = 1 \times 294 + 66, \quad 294 = 4 \times 66 + 30\) | ||
| \(66 = 2 \times 30 + 6, \quad 30 = 5 \times 6 + 0\) | A1 | 1.1b |
| So HCF(2 322, 654) = 6 | A1 | 1.1b |
| (3) | ||
| (5 marks) |
Notes
M1: Uses the Euclidean algorithm showing two stages (Must be Euclidean algorithm not e.g. using prime factors)
A1: Completes the algorithm correctly
A1: All correct and concludes HCF is 6