Question

Prime factorize 265.

Answer 1

Hint: In this problem, we have to find the prime factors of the given number 265. We know that the given number 265 is a composite number and therefore it will have prime factors. We can now see how to calculate the prime factors of the given number. We can first divide the given number 265 with the smallest prime factor, here we can take 5. We can keep dividing until it gives a non-zero remainder and we can find the prime factors.

Complete step by step answer:
Here we have to find the prime factors of the given number 265.
We know that the given number 265 is a composite number and therefore it will have prime factors. We can now see how to calculate the prime factors of the given number.
We can first divide the given number 265 with the smallest prime factor, here we can take 5, we get
\[\Rightarrow 265\div 5=53\]
\[\begin{align}
  & 5\overset{53}{\overline{\left){\underline{\begin{align}
  & 265 \\
 & 25 \\
\end{align}}}\right.}} \\
 & \text{ 1}5 \\
 & \text{ }\underline{15} \\
 & \text{ 0} \\
\end{align}\]
Here we have 53 as quotient but we have the remainder as 0. So, we can divide 53 again to get a non-zero remainder.
\[\begin{align}
  & 5\overset{1}{\overline{\left){\underline{\begin{align}
  & 53 \\
 & 5 \\
\end{align}}}\right.}} \\
 & \text{ 3} \\
\end{align}\]
Here we have a non-zero remainder and we cannot further divide the numbers.
The prime factors of 256 can be written as,
\[\Rightarrow {{5}^{1}}\times {{53}^{1}}\]
Therefore, the prime factors of 265 are 5 and 53.

Note: We should always remember that 265 has four factors, they are 1, 5, 53, 265 in which 5 and 53 are the prime factors. We should remember that prime factors are nothing but the number which are prime. We can also find the factors for the given number and take out the prime numbers which will be the prime factors.