Integer reasoning
Objective. Solve multi-step puzzles involving factors, powers and directed numbers.
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- 2. Worked example
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Learn: the key idea
Integer reasoning uses facts about factors, multiples, powers and directed numbers together to solve multi-step puzzles where the route to the answer is not immediately obvious. A typical approach is to list possibilities that satisfy one clue, such as factors of a number, then test each against the remaining clues until only one value survives. For example, finding a number that is a factor of 24 and also a square number narrows the options to 1 and 4. Working systematically and checking every clue prevents missing a valid solution or accepting an invalid one.
Worked example
A number is a factor of 48, is greater than 1, and is a cube number. Use integer reasoning to find it.
- 1List factors of 48 greater than 1: 2, 3, 4, 6, 8, 12, 16, 24, 48
- 2List cube numbers: 1, 8, 27, 64
- 3Compare the two lists to find a common value
- 4The only common value is 8
Answer: 8
Concept mastery
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Practice
Practice happens on its own screen, one question at a time. Answers stay hidden until you submit yours, and you can stop and pick up at the same question later.
Start practisingCommon mistake. Pupils often stop after satisfying the first clue in a puzzle and forget to check later clues, such as picking 8 as a factor of 24 that is even, without checking it must also be a square number, giving a wrong final answer.
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