Stage 8 - Q1 - 2 marks
Find the highest common factor.
Hint
Decide whether a common divisor or a common multiple is needed.
Stage 8 - Q2 - 2 marks
Find the highest common factor.
Hint
Decide whether a common divisor or a common multiple is needed.
Stage 8 - Q3 - 3 marks
Find the lowest common multiple.
Hint
Decide whether a common divisor or a common multiple is needed.
Stage 8 - Q4 - 3 marks
Find the lowest common multiple.
Hint
Decide whether a common divisor or a common multiple is needed.
Stage 8 - Q5 - 4 marks
60 blue cards and 64 green cards fill the greatest possible number of identical packs. None remain. Find the number of packs and their contents.
Hint
Decide whether a common divisor or a common multiple is needed.
Stage 8 - Q6 - 4 marks
Two signals flash every 18 seconds and every 96 seconds. They flash together now. When do they next flash together?
Hint
Decide whether a common divisor or a common multiple is needed.
Stage 8 - Q7 - 5 marks
Find every positive integer n below 60 for which HCF(36, \(n)=12\).
Hint
List multiples of 12 first, then test the HCF.
Stage 8 - Q8 - 5 marks
Two lights flash every 12 and 18 seconds. They flash together at time 0. How many further simultaneous flashes occur during the next five minutes?
Hint
Find the repeating joint period. Do not count the flash at time 0.
Stage 8 - Q9 - 5 marks
Can two positive integers have HCF 12 and LCM 90? Justify your answer without trying every pair.
Hint
Must the HCF divide the LCM? Explain why.
Stage 8 - Q10 - 5 marks
Two positive integers have HCF 6 and LCM 180. Find every possible unordered pair.
Hint
Remove the common factor 6 first. What must the two remaining numbers have in common?