Foundation November 2022 Paper 3 Q14
14
(a) An integer between 70 and 80 is written as the product of its prime factors as \(2 \times 3 \times f\).
Find the value of \(f\) and the integer.
\(f =\) ....................
Integer = .................... [3]
(b) 98 and 147 are written as the product of their prime factors.\[98 = 2 \times 7^2 \qquad 147 = 3 \times 7^2\]
Work out the highest common factor (HCF) of 98 and 147. [2]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 13 and 78 | 3 | B2 for answer 13 or 78 in correct place or M1 for one correct trial of \(2 \times 3 \times\) prime or a correct factor tree for a number from 70 to 80 or an integer from 70 to 80 \(\div (2 \times 3)\) | Accept 6 for \((2 \times 3)\) throughout e.g. \(6 \times 13 = 78\) for \(2 \times 3 \times 13 = 78\) e.g. \(2 \times 3 \times 5 = 30\), \(2 \times 3 \times 7 = 42\), \(2 \times 3 \times 11 = 66\) May be \(2 \times 3 \times 13 = 78\) if answer not 13 and 78 Includes 70 and 80 |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 49 | 2 | B1 for answer 7 | Accept \(7^2\) for 2 marks |