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07 Jun 2022, 23:36
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Hi,
If a number less than 100 is not divisible by any prime divisor less than 10, then the number has to be prime. And, of course, the only prime divisors less than 10 are 2, 3, 5, and 7. So those are the only divisors we have to check. It's not divisible by any of those numbers, it is a prime number. So for example, here's a practice problem.
Then what about those bigger than 100, and why?
Thanks a lot in advance
If a number less than 100 is not divisible by any prime divisor less than 10, then the number has to be prime. And, of course, the only prime divisors less than 10 are 2, 3, 5, and 7. So those are the only divisors we have to check. It's not divisible by any of those numbers, it is a prime number. So for example, here's a practice problem.
Then what about those bigger than 100, and why?
Thanks a lot in advance
08 Jun 2022, 15:24
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arbre
Hi,
If a number less than 100 is not divisible by any prime divisor less than 10, then the number has to be prime. And, of course, the only prime divisors less than 10 are 2, 3, 5, and 7. So those are the only divisors we have to check. It's not divisible by any of those numbers, it is a prime number. So for example, here's a practice problem.
Then what about those bigger than 100, and why?
Thanks a lot in advance
If a number less than 100 is not divisible by any prime divisor less than 10, then the number has to be prime. And, of course, the only prime divisors less than 10 are 2, 3, 5, and 7. So those are the only divisors we have to check. It's not divisible by any of those numbers, it is a prime number. So for example, here's a practice problem.
Then what about those bigger than 100, and why?
Thanks a lot in advance
Hi arbre,
When multiplying two positive integers together to get a larger, third number, there are a number of relationships that will exist. If the two numbers are EQUAL, then you have a 'perfect square' - for example (10)(10) = 100. In all other cases though, with that same result (in this case, 100), ONE of the two starting numbers will be LESS than 10 and ONE will be GREATER than 10 (for example (5)(20) or (4)(25)).
The pattern that you're asking about is in regards to Prime Factorization (re: the idea that every positive integer greater than 1 is either a Prime number or the product of some Primes). Since 10^2 = 100, with any number LESS than 100, if we're looking to see whether the number is Prime or not, we'll only need to divide by 2, 3, 5 and/or 7 - since the next prime is 11 and 11^2 = 121 (which is too big - and if 11 is one of the Prime Factors in the number, then we'll find it by dividing by one of the smaller primes).
For any number that is GREATER than 100, we may need to consider larger primes, but we can use perfect squares - along with this concept - to determine which, if any, additional calculations are required. For example, with 143 - and the knowledge that 11^2 = 121, we need to consider dividing by 11 (along with 2, 3, 5 and 7) to determine whether 143 is prime or not.
GMAT assassins aren't born, they're made,
Rich
Contact Rich at: Rich.C@empowergmat.com
08 Jun 2022, 22:53
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arbre
Hi,
If a number less than 100 is not divisible by any prime divisor less than 10, then the number has to be prime. And, of course, the only prime divisors less than 10 are 2, 3, 5, and 7. So those are the only divisors we have to check. It's not divisible by any of those numbers, it is a prime number. So for example, here's a practice problem.
Then what about those bigger than 100, and why?
Thanks a lot in advance
If a number less than 100 is not divisible by any prime divisor less than 10, then the number has to be prime. And, of course, the only prime divisors less than 10 are 2, 3, 5, and 7. So those are the only divisors we have to check. It's not divisible by any of those numbers, it is a prime number. So for example, here's a practice problem.
Then what about those bigger than 100, and why?
Thanks a lot in advance
To understand this concept, check out these two blog posts:
https://anglesandarguments.com/blog-details/23
https://anglesandarguments.com/blog-details/31
