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17 May 2019, 06:54
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Hello,
Greetings for the day!
This is the fourth and the final part of our post on Prime numbers. We hope that you have all liked the first three parts of this post and found it useful.
Just in case you have not gone through them, here are the links to those posts:
Part 1 -https://bit.ly/2Yu4JMY
Part 2 -https://bit.ly/2WPWMS6
Part 3 -https://bit.ly/30nWL9X
In yesterday’s post, we discussed about the applications of Prime numbers and also a smart way of prime factorizing large numbers to save time.
Today’s post is where we would like to summarize everything there is, to this discussion, so that you have the important concepts on Prime numbers in one place. Additionally, we would be posting some good questions which involve Prime numbers, towards the end of this post.
So, here we go. Summarizing our discussion on Prime numbers,
1. A prime number has to be a positive integer.
2. A prime number has exactly 2 factors – neither more nor less.
3. 1 is not a prime number. It is just an ODD number.
4. 2 is the first prime number and the only even prime number.
5. Except 2, all other prime numbers are odd.
6. Except 2,3,5 and 7, all other prime numbers always end with 1 or 3 or 7 or 9. But, all numbers ending with 1 or 3 or 7 or 9 need not necessarily be prime.
7. Any prime number greater than 3 can always be written in the form of (6k) -1 or (6k) + 1 where k is a positive integer. But all numbers which can be written in the form of (6k) – 1 or (6k) + 1 need not necessarily be prime.
8. To check for primes, you can divide the given number by numbers like 3, 9 and 11 which have simple divisibility rules, especially if the number is a fairly large 3-digit or 4-digit number.
9. Alternatively, observe the answer options to check if the values give you a clue about the number being prime or non-prime.
10. For smaller 3-digit numbers, you can use the square root method to find out if the given number is prime.
11. The most important application of prime numbers is in the Prime factorization process. The prime factorization process forms the backbone for topics like HCF & LCM, number of factors and factorials.
12. Questions related to Prime number concepts can turn up from any area of Math.
We hope that you found this post on prime numbers highly informative and yet, simple to comprehend. We will end this post with a few questions for you to answer and help you consolidate your learnings.
https://gmatclub.com/forum/if-p-is-a-multiple-of-7-and-p-a-3-b-296041.html
https://gmatclub.com/forum/x-is-a-positive-integer-is-x-1-1-divisible-by-x-296042.html
https://gmatclub.com/forum/if-p-and-q-are-positive-integers-is-p-q-also-an-integer-296045.html
See you in our next post on another interesting aspect of GMAT Quant.
Thank you!
Greetings for the day!
This is the fourth and the final part of our post on Prime numbers. We hope that you have all liked the first three parts of this post and found it useful.
Just in case you have not gone through them, here are the links to those posts:
Part 1 -https://bit.ly/2Yu4JMY
Part 2 -https://bit.ly/2WPWMS6
Part 3 -https://bit.ly/30nWL9X
In yesterday’s post, we discussed about the applications of Prime numbers and also a smart way of prime factorizing large numbers to save time.
Today’s post is where we would like to summarize everything there is, to this discussion, so that you have the important concepts on Prime numbers in one place. Additionally, we would be posting some good questions which involve Prime numbers, towards the end of this post.
So, here we go. Summarizing our discussion on Prime numbers,
1. A prime number has to be a positive integer.
2. A prime number has exactly 2 factors – neither more nor less.
3. 1 is not a prime number. It is just an ODD number.
4. 2 is the first prime number and the only even prime number.
5. Except 2, all other prime numbers are odd.
6. Except 2,3,5 and 7, all other prime numbers always end with 1 or 3 or 7 or 9. But, all numbers ending with 1 or 3 or 7 or 9 need not necessarily be prime.
7. Any prime number greater than 3 can always be written in the form of (6k) -1 or (6k) + 1 where k is a positive integer. But all numbers which can be written in the form of (6k) – 1 or (6k) + 1 need not necessarily be prime.
8. To check for primes, you can divide the given number by numbers like 3, 9 and 11 which have simple divisibility rules, especially if the number is a fairly large 3-digit or 4-digit number.
9. Alternatively, observe the answer options to check if the values give you a clue about the number being prime or non-prime.
10. For smaller 3-digit numbers, you can use the square root method to find out if the given number is prime.
11. The most important application of prime numbers is in the Prime factorization process. The prime factorization process forms the backbone for topics like HCF & LCM, number of factors and factorials.
12. Questions related to Prime number concepts can turn up from any area of Math.
We hope that you found this post on prime numbers highly informative and yet, simple to comprehend. We will end this post with a few questions for you to answer and help you consolidate your learnings.
https://gmatclub.com/forum/if-p-is-a-multiple-of-7-and-p-a-3-b-296041.html
https://gmatclub.com/forum/x-is-a-positive-integer-is-x-1-1-divisible-by-x-296042.html
https://gmatclub.com/forum/if-p-and-q-are-positive-integers-is-p-q-also-an-integer-296045.html
See you in our next post on another interesting aspect of GMAT Quant.
Thank you!
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block below for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
09 Jan 2021, 12:05
Kudos
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Automated notice from GMAT Club BumpBot:
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This post was generated automatically.
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
