Name: Prime Numbers & Prime Factorisation
Uploaded: 2019-07-19
Duration: 6 min 40 s
Description: In this video, we will learn the concept of factors, prime numbers, and prime factorisation methods of finding numbers with examples.

Question

In a

3

-digit prime number, sum of its digits is

5

. If the ones and hundreds digits are interchanged, it still remains prime number. What is the original number and what is the changed number ?

Accepted Answer

We know that the prime number is a number that can be divided by $1$ and the number itself.

The last digit has to be odd, else we will not get a $3$ digit prime number. So, the possible last digits are : $1, 3, 5, 7$ or $9$ .

Now, the unit's digit $5, 7$ or $9$ is not possible because sum of the digits is $5$ .

So, the unit's digit is either $1$ or $3$

Now, let us see the different possible numbers with $1$ as the unit's digit.

$131 \to$ It is a prime number and remains prime if the ones and hundreds digits are interchanged.

$311 \to$ It is a prime number and remains prime if the ones and hundreds digits are interchanged.

$221 \to$ It is not a prime number,

$401 \to$ It is a prime number but, does not remain prime if the ones and hundreds digits are interchanged.

The different numbers with $3$ as unit's digit

$113 \to$ It is a prime number and remains prime if the ones and hundreds digits are interchanged.

$203 \to$ It is not a prime number,

Therefore, the original numbers could be $131, 311$ or $113$ and their respective changed numbers will be $131, 113$ and $311$ .

Dr. Sanjeev Verma and R.K. Tyagi Solutions for Chapter: Playing With Whole Numbers, Exercise 14: VALUE-BASED QUESTIONS

Dr. Sanjeev Verma Mathematics Solutions for Exercise - Dr. Sanjeev Verma and R.K. Tyagi Solutions for Chapter: Playing With Whole Numbers, Exercise 14: VALUE-BASED QUESTIONS

Questions from Dr. Sanjeev Verma and R.K. Tyagi Solutions for Chapter: Playing With Whole Numbers, Exercise 14: VALUE-BASED QUESTIONS with Hints & Solutions

Learn and Prepare for any exam you want !