Question

Prime factorization of \[13915\] is ___________.
A. \[5 \times 11 \times 11 \times 23\]
B. \[5 \times 11 \times 7 \times 23\]
C. \[11 \times 7 \times 23 \times 3\]
D. \[5 \times 11 \times 11 \times 3\]

Answer 1

Hint: In this question we have prime factorized the given number. First we have to know what is a method of prime factorization of a number?
The method of prime factorization is used to “break down” or express a given number as a product of prime numbers. More so, if a prime number occurs more than once in the factorization, it is usually expressed in exponential form to make it look more compact.
We need to follow certain steps:
For any given number, test if it is divisible by the smallest prime number which is 2.
Check again if the other number that comes out is divisible by 2. If it is, keep going until the new number is no longer divisible by 2.
In this way we can solve the problem.

Complete step-by-step answer:
It is given that; the given number is \[13915\].
We have to find the prime factorization of the given number.
The method of prime factorization is used to “break down” or express a given number as a product of prime numbers. More so, if a prime number occurs more than once in the factorization, it is usually expressed in exponential form to make it look more compact.
We need to follow few steps to find the factorization:
\[ \Rightarrow 13915\]
Step 1: Since, the last digit is 5, we will divide the number by 5.
\[ \Rightarrow 5 \times 2783\]
After division if the number is composite, we will continue the division by prime numbers. Otherwise the division will stop there.
\[ \Rightarrow 5 \times 2783\]
Step 2: We will continue the division using prime numbers until we will not get a prime number.
For the given number after factorized by 5, again we can factorize the remain term by the prime factor $11$ we get,
\[ \Rightarrow 5 \times 11 \times 253\]
Step 3: At last we will express the number in the multiplicative form of prime numbers.
\[ \Rightarrow 5 \times 11 \times 11 \times 23\]
Hence, the prime factorization of the given number \[13915\] is \[5 \times 11 \times 11 \times 23\].

So, the correct answer is “Option A”.

Note: There are some other methods to find the prime factorization. These are: division method, factor tree method.
If we apply these processes, we can get the same answer.
A prime number is a whole number greater than 1 that is only divisible by 1 and itself. In other words we can say that a prime number has exactly two factors: 1 and itself.
For prime factorization we must divide the number by prime numbers only.