whole numbers dividing 60

sufinaz

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how many whole positive numbers you can think of divides 60, answers whole number again?
 

MarkFL

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Can you list all the factor pairs?
 

pka

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\(\displaystyle 60=2^2\cdot 3\cdot 5\).
 

sufinaz

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1,2,3,5,4,6,10,15,,20,30,60 that's all I guess but there is 12 number, is that what it's asking?
 

Subhotosh Khan

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sufinaz

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is the answer 13 than?
 

sufinaz

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oh dear, thanks
 

pka

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is the answer 13 than?
No the answer is 12.
Let me give you the general rule:
Write the number in factored form, like \(\displaystyle N=(p_1)^{n_1}\cdot(p_2)^{n_2}\cdot(p_3)^{n_3}\cdots(p_k)^{n_k}\) where each \(\displaystyle p_j\) is a prime factor and each \(\displaystyle n_j\in\mathbb{Z}^+~\&~n_j\ge 1\)
then the number of divisors of \(\displaystyle N\) is \(\displaystyle (n_1+1)\cdot(n_2+1)\cdot(n_3+1)\cdots(n_k+1)\)
 
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