Higher June 2022 Paper 6 Q17
17 Blake is asked to write 15 552 000 000 as a product of prime factors in index form.
Blake writes
\[15\,552\,000\,000 = 2^7 \times 5^6 \times 6^5\](a) Explain Blake’s mistake. [1]
(b) Write 15 552 000 000 as a product of prime factors in index form. [2]
(c) You are given that \(140\,000 = 2^5 \times 5^4 \times 7\).
Find the highest common factor (HCF) of 15 552 000 000 and 140 000. [2]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 6 is not a prime number oe | 1 | See Appendix | |
Appendix: exemplar responses for Q17(a)
| Reason | Judgement | Mark |
|---|---|---|
| 6 is not a prime number | 1 | |
| 6 is not a prime factor | 1 | |
| 6 can be written as 2 × 3 | 1 | |
| 6 is not allowed | 0 |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| \(2^{12} \times 3^5 \times 5^6\) | 2 | M1 for [\(6^5 =\)] \(2^5 \times 3^5\) seen, expanded or used or for answer including \(2^{12}\) or \(3^5\) | Correct answer in expanded form implies \(2^5 \times 3^5\) used for M1 |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 20 000 | 2 | B1 for \(2^5 \times 5^4\) | |