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a-b-N-a-b-144-how-many-different-numbers-can-a-and-b-be-here-




Question Number 211722 by hardmath last updated on 18/Sep/24
a, b ∈ N  a ∙ b = 144    how many different numbers can a and b be here?
$$\mathrm{a},\:\mathrm{b}\:\in\:\mathbb{N} \\ $$$$\mathrm{a}\:\centerdot\:\mathrm{b}\:=\:\mathrm{144} \\ $$$$ \\ $$how many different numbers can a and b be here?
Answered by mehdee7396 last updated on 18/Sep/24
144=2^4 ×3^2   ans=5×3−1=14 ✓
$$\mathrm{144}=\mathrm{2}^{\mathrm{4}} ×\mathrm{3}^{\mathrm{2}} \\ $$$${ans}=\mathrm{5}×\mathrm{3}−\mathrm{1}=\mathrm{14}\:\checkmark \\ $$$$ \\ $$

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