
The numbers 13 and 31 are prime numbers. Both these numbers have the same digits 1 and 3. Find such pairs of prime numbers up to 100.
Answer
516.3k+ views
4 likes
Hint: At first, collect and write all the numbers between 1 to 100 and then we observe one by one and see that there are a total of three pairs just like the pair 13 and 31.
Complete step-by-step answer:
In the question, we are said that both 13 and 31 prime numbers and both these numbers have the same digits 1 and 3 and thus, we have to find such pairs.
Before proceeding let us know about some information.
The divisors of natural number n are the natural number that divides n evenly. Every natural number has both 1 and itself as a divisor and if a number has no divisor other than 1 and itself it is considered as prime otherwise, it is considered as composite. Now, let's consider examples like 5, its factors are only 1 and 5, so, it’s a prime number, while, for 4 it's factors are 1 and 4 as well as 2. Hence, it is considered as composite.
So, we will first write down all the prime numbers between 1 and 100.
The primes are:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.
Here pairs are:
13 and 31, 17 and 71, 37 and 73.
The pairs except 13 and 31 are 17 and 71, 37 and 73.
Note: Generally, students miss out factors while finding whether a number is prime or composite. So, for a given number n, one should check for the factors up to value. From this, we can also say that we can avoid the numbers ending in 0, 2, 4, 6 and 8 or even numbers in general as they will have factors.
Complete step-by-step answer:
In the question, we are said that both 13 and 31 prime numbers and both these numbers have the same digits 1 and 3 and thus, we have to find such pairs.
Before proceeding let us know about some information.
The divisors of natural number n are the natural number that divides n evenly. Every natural number has both 1 and itself as a divisor and if a number has no divisor other than 1 and itself it is considered as prime otherwise, it is considered as composite. Now, let's consider examples like 5, its factors are only 1 and 5, so, it’s a prime number, while, for 4 it's factors are 1 and 4 as well as 2. Hence, it is considered as composite.
So, we will first write down all the prime numbers between 1 and 100.
The primes are:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.
Here pairs are:
13 and 31, 17 and 71, 37 and 73.
The pairs except 13 and 31 are 17 and 71, 37 and 73.
Note: Generally, students miss out factors while finding whether a number is prime or composite. So, for a given number n, one should check for the factors up to
Latest Vedantu courses for you
Grade 9 | CBSE | SCHOOL | English
Vedantu 9 CBSE Pro Course - (2025-26)
School Full course for CBSE students
₹37,300 per year
Recently Updated Pages
Master Class 8 Science: Engaging Questions & Answers for Success

Master Class 8 English: Engaging Questions & Answers for Success

Master Class 8 Social Science: Engaging Questions & Answers for Success

Master Class 8 Maths: Engaging Questions & Answers for Success

Class 8 Question and Answer - Your Ultimate Solutions Guide

Master Class 11 Physics: Engaging Questions & Answers for Success

Trending doubts
What is the southernmost point of the Indian Union class 8 social science CBSE

How many ounces are in 500 mL class 8 maths CBSE

Name the states through which the Tropic of Cancer class 8 social science CBSE

List some examples of Rabi and Kharif crops class 8 biology CBSE

How many ten lakhs are in one crore-class-8-maths-CBSE

Explain land use pattern in India and why has the land class 8 social science CBSE
