a is a factor of 10 and b is a factor of 15. (text(Column A))/(text(The smallest value that ab must be a factor of))(text(Column B))/(30) Is Column A greater than/ smaller than / equal to Column B?

Alfredeim

Alfredeim

Answered question

2022-09-07

a is a factor of 10 and b is a factor of 15.
Column A Column B The smallest value that ab must be a factor of 30
Is Column A greater than/ smaller than / equal to Column B?

Answer & Explanation

Azul Lang

Azul Lang

Beginner2022-09-08Added 20 answers

Step 1
The answer is 150 which is greater than 30, we must include the case when a = 10 and b = 15 (since the question doesn't explicitly ask us to use only non-trivial divisors). A justification of the above statement is as follows:
The set of all possible values for the product ab is { 1 , 2 , 3 , 5 , 6 , 10 , 15 , 25 , 30 , 50 , 75 , 150 } . Now suppose the smallest value that ab must be a factor of were less than 150, take for instance that it was 75, then if a b = 150 , we'd have the contradiction that 150 is not a factor of 75. We can extend this line of reasoning to any other number < 150 . Thus the only number that satisfies the requirements is 150.

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