How do you write 98 as a product of prime factors?

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Explanation:

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Nov 19, 2016

$98 = 2 \cdot 7 \cdot 7$

Explanation:

Since $98$ ends with an even digit, we can tell that it is divisible by $2$:

$\frac{98}{2} = 49$

Try each possible prime factor in turn:

• $49$ ends in an odd digit, so is not divisible by $2$.

• The sum of its digits is $4 + 9 = 13$, which is not divisible by $3$, so $49$ is not divisible by $3$ either.

• $49$ does not ends with $5$ or $0$, so is not divisible by $5$.

• $49$ is divisible by $7$. We find:

$\frac{49}{7} = 7$

So:

$98 = 2 \cdot 7 \cdot 7$

We can also draw this as a factor tree:

$\textcolor{w h i t e}{00000} 98$
$\textcolor{w h i t e}{0000} \text{/"color(white)(00)"\}$
$\textcolor{w h i t e}{000} 2 \textcolor{w h i t e}{000} 49$
$\textcolor{w h i t e}{000000} \text{/"color(white)(00)"\}$
$\textcolor{w h i t e}{00000} 7 \textcolor{w h i t e}{0000} 7$

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