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Factors Multiples LCM and HCF — Free MYP3 Mathematics Practice Questions
1QuestionFinding Factors of a NumberConcept Practice
2 marks~3 minCriterion A
A rectangle has an area of 36 square units. Its length and width are both whole numbers, so .
List all possible pairs where . [2]
List all possible pairs where . [2]
Solutions
2QuestionFinding Factors of a NumberAssessment Practice
6 marks~9 minCriterion C
A student designs a rectangular garden with an area of . She lists all whole-number dimension pairs:
She claims there are exactly 9 possible designs.
| Length (m) | 1 | 2 | 3 | 4 | 6 | 9 | 12 | 18 | 36 |
|---|---|---|---|---|---|---|---|---|---|
| Width (m) | 36 | 18 | 12 | 9 | 6 | 4 | 3 | 2 | 1 |
She claims there are exactly 9 possible designs.
a
State how many distinct rectangular designs are actually possible, and list them. [2]
b
Explain why the number of possible dimension pairs is no longer limited to whole numbers when measurements have a precision of . Give one example of a valid non-integer pair. [3]
c
Analyse one real-world constraint, other than measurement precision, that could further limit the possible dimensions of the garden. Justify your answer. [1]
Solutions
3QuestionFinding Factors of a NumberConcept Practice
2 marks~3 minCriterion B
The factor pairs of 24 are shown below.
Row 1:
Row 2:
Each number in Row 1 is paired with the number directly below it in Row 2.
Row 1:
Row 2:
Each number in Row 1 is paired with the number directly below it in Row 2.
a
Describe the pattern you observe in the product of each factor pair of 24. [1]
b
Apply this pattern to find all factor pairs of 36. [1]
Solutions
4QuestionFinding Factors of a NumberAssessment Practice
6 marks~9 minCriterion D
A school principal needs to organise 48 students into equal-sized groups for a rotation activity. Each group size must be a factor of 48. The table below shows some information about available resources.
Number of teachers available: 6
Maximum room capacity: 20 students
Minimum group size (safety ratio): 4 students
Number of teachers available: 6
Maximum room capacity: 20 students
Minimum group size (safety ratio): 4 students
a
List all factors of 48. [2]
b
Explain why group sizes of 1 and 48 are not suitable for this rotation activity. [2]
c
Using the resource information, identify all feasible group sizes and justify which group size you would recommend. [2]
Solutions
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