Question

How do you write 850 as the product of its prime factors?

Answer 1

Hint: To write 850 as a product of its prime factors. First of all, we will divide 850 by the smallest prime number then we divide in such a way by moving from the smallest to greater prime numbers. And we will divide 850 in such a way till we get the number 1.

Complete step by step answer:
The number which we have to write it as product of its prime factors as follows:
850
As you can see that the above number is even so we are going to divide the above number by 2 first.
$2\overset{425}{\overline{\left){\begin{align}
  & 850 \\
 & \dfrac{8}{\begin{align}
  & 05 \\
 & \dfrac{-4}{\begin{align}
  & 10 \\
 & \dfrac{10}{00} \\
\end{align}} \\
\end{align}} \\
\end{align}}\right.}}$
The quotient of the above division is 425. Now, this number is divisible by 5 so dividing 425 by 5 we get,
$5\overset{85}{\overline{\left){\begin{align}
  & 425 \\
 & \dfrac{40}{\begin{align}
  & 025 \\
 & \dfrac{025}{000} \\
\end{align}} \\
\end{align}}\right.}}$
The quotient of the above division is 85 so we are going to divide 85 by 5 we get,
$5\overset{17}{\overline{\left){\begin{align}
  & 85 \\
 & 5 \\
 & \overline{\begin{align}
  & 35 \\
 & \dfrac{35}{00} \\
\end{align}} \\
\end{align}}\right.}}$
The quotient of the above division is 17.Now, 17 is itself a prime number so 17 is divided by 17 will give 1.
$17\overset{1}{\overline{\left){\begin{align}
  & 17 \\
 & \dfrac{17}{00} \\
\end{align}}\right.}}$
Hence, the prime factorization of 850 is calculated by multiplying all the divisors of the above division which is equal to:
$850=2\times 5\times 5\times 17$

Note: We can check whether the product of prime factorization which we have found above is equal to 850 or not. The method is simple, we just have to multiply all the prime factors and whether the product is equal to 850 or not.