Nice approach. A question and a thought. It would be great if you could explain why testing up to the square root of the number matters. I'm guessing that if a number is composite, it has two or more divisors, and it can't have divisors that are both larger than its square root. Thus any composite number has at least one prime factor lower than its own square root. Am I right? If so, sharing things like that will make better videos. Second, there are two quick checks that you can do faster than taking a square root. One is that there are tricks for knowing that a number is a multiple of certain primes: 2 - Is the number even? (as you said) 3 - Do the digits add up to three? If and only if so, the number is divisible by three 5 - The number ends in zero or 5. The other trick is to take the possible prime, X, and add one, and also subtract one. If neither X + 1 nor X - 1 is divisible by 6, then the number (for all numbers greater than three) is not prime. I would do these quick checks before calculating the square root for a thorough test.
Hi! Yes it is true that there are more details that can be included in the video. I teach math full time and sometimes it is hard to find a balance between providing enough information to solve the problem and including details like you mentioned in this comment. In general, I think the extra tricks you mention are critical for students prepping for a timed standardized test (the GMAT is notorious for being long and students really need time saving tricks) but for a student in a standard classroom this is less critical. In answer to your comment about why the method works: Yes you have it right. All composite numbers can be written as a product of prime numbers (this is called the prime factorization) and any factors larger than the square root will have a corresponding factor smaller than the square root. (For example 51= 3 times 17. 17 is larger than the square root of 51 but the corresponding factor, 3, is smaller). Thanks for watching!
lol good question! I read a lot and have found that I sometimes mispronounce words because I have never heard any one say them! In this instance I am fairly confident that I am using standard American pronunciation. 😁
Nice approach. A question and a thought.
It would be great if you could explain why testing up to the square root of the number matters. I'm guessing that if a number is composite, it has two or more divisors, and it can't have divisors that are both larger than its square root. Thus any composite number has at least one prime factor lower than its own square root. Am I right? If so, sharing things like that will make better videos.
Second, there are two quick checks that you can do faster than taking a square root.
One is that there are tricks for knowing that a number is a multiple of certain primes:
2 - Is the number even? (as you said)
3 - Do the digits add up to three? If and only if so, the number is divisible by three
5 - The number ends in zero or 5.
The other trick is to take the possible prime, X, and add one, and also subtract one. If neither X + 1 nor X - 1 is divisible by 6, then the number (for all numbers greater than three) is not prime.
I would do these quick checks before calculating the square root for a thorough test.
Hi! Yes it is true that there are more details that can be included in the video. I teach math full time and sometimes it is hard to find a balance between providing enough information to solve the problem and including details like you mentioned in this comment. In general, I think the extra tricks you mention are critical for students prepping for a timed standardized test (the GMAT is notorious for being long and students really need time saving tricks) but for a student in a standard classroom this is less critical.
In answer to your comment about why the method works:
Yes you have it right. All composite numbers can be written as a product of prime numbers (this is called the prime factorization) and any factors larger than the square root will have a corresponding factor smaller than the square root. (For example 51= 3 times 17. 17 is larger than the square root of 51 but the corresponding factor, 3, is smaller).
Thanks for watching!
I pronounce "composite" completely differently to you. Who's right..?
lol good question! I read a lot and have found that I sometimes mispronounce words because I have never heard any one say them! In this instance I am fairly confident that I am using standard American pronunciation. 😁
Are you okay? (This is genuine, bc im rlly concerned that you haven't posted in a while yet.)
Hi! Yes I am doing well. I’m on summer break taking some time off before we hit the ground running in the fall! ❤️
*_3rd_* comment -- prime (i think)
Hi! 1233 is not actually a prime. It is divisible by 3. ☺️