Hint
Use the stated units and precision. Divide repeatedly by 2, or use a factor tree.
Worked solution
(a)
Repeated prime division gives these complete factorisations.
Answer: \(N=2^{5}3^{2},\quad M=2^{4}3^{3}5^{2}\)
(b)
Use the smaller prime exponents.
\(144\)
Answer: \(144\)
(c)
Use the larger prime exponents.
\(21600\)
Answer: \(21600\)
Maths4U indicative marking guidance
Maths4U indicative marking guidance, not an official mark scheme. Credit complete valid alternative methods and consequential reasoning. An unexplained result does not earn a method mark.
(a) · 2 marks
- 1 mark: Decompose each positive integer completely into prime factors.
- 1 mark: Give the complete requested result, using the required units, precision and boundary inclusion.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: Keep intermediate values exact until the final step.
(b) · 2 marks
- 1 mark: Use the smaller prime exponents.
- 1 mark: Give the correct requested result, retaining signs, units and any domain restrictions.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: Check the answer against the original conditions.
(c) · 2 marks
- 1 mark: Use the larger prime exponents.
- 1 mark: Give the correct requested result, retaining signs, units and any domain restrictions.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: Keep intermediate values exact until the final step.
Total: 6 marks.