Question

What is the prime factorization of 1260?

Answer 1

Hint: From the question given we have to find the prime factorization of 1260. As we know that the prime factorization means to express a number in the multiples of the prime number. To find this first we will divide the number with the least prime number which can be divided and we continue the process until the last quotient is 1 or any prime number.

Complete step-by-step solution:
From the question given we have to find the prime factorization of 1260,
As we know that the prime factorization means to express a number in the multiples of the prime number. To find this first we will divide the number with the least prime number which can be divided and we continue the process until the last quotient is 1 or any prime number.
Now, coming to the given question the number 1260 is even so it will be divided by least prime number 2,
$\Rightarrow \dfrac{1260}{2}=630$
Now, the quotient is 630 it is also a even number so it will be divided by least prime number 2,
$\Rightarrow \dfrac{630}{2}=315$
Now, the quotient is 315 it is an odd number so it will be divided by least prime number 3,
$\Rightarrow \dfrac{315}{3}=105$
Now, the quotient is 105 it is an odd number so it will be divided by least prime number 3,
$\Rightarrow \dfrac{105}{3}=35$
Now, the quotient is 105 it is an odd number so it will be divided by least prime number 5, because it is not divisible by 3,
$\Rightarrow \dfrac{35}{5}=7$
Now, as we have obtained our quotient as a prime number, we will not factorize it further.
Thus, the factors of 1260 in terms of prime numbers are $2,2,3,3,5,7$.
Therefore, the prime factorization of 1260 is
$\Rightarrow 1260={{2}^{2}}\times {{3}^{2}}\times 5\times 7$

Note: Students must be very careful in doing the calculations. Students should know the definition of prime factorization, it is used widely to find the least common multiple that is LCM and greatest common factor that is GCF.
We can also do the solution as follows.
$\begin{align}
  & \Rightarrow 2\left| \!{\underline {\,
  1260 \,}} \right. \\
 & \text{ 3}\left| \!{\underline {\,
  630 \,}} \right. \\
 & \text{ 5}\left| \!{\underline {\,
  210 \,}} \right. \\
 & \text{ 7}\left| \!{\underline {\,
  42 \,}} \right. \\
 & \text{ 3}\left| \!{\underline {\,
  6 \,}} \right. \\
 & \text{ 2}\left| \!{\underline {\,
  2 \,}} \right. \\
 & \text{ 1} \\
\end{align}$
Therefore, the prime factorization of 1260 is
$\Rightarrow 1260={{2}^{2}}\times {{3}^{2}}\times 5\times 7$