October 9th Math Review

Do you remember the handy rules for division? Here they are, for review. Since calculators aren't allowed during the GRE, I have to practice and increase my time with basic math.

• An interger can be divided by 2 if the units digit (the last digit of the number) can be divided by 2.
• An interger can be divided by 3 if the sum of its digits can be divided by 3.
• An interger can be divided by 4 if the last two digits form a number that can be divided by 4.
• An interger can be divided by 5 it the units digit is 0 or 5.
• An interger can be divided by 6 if it is divisble by both 2 and 3.
• I don't know a rule for 7 or 8. Do you? Oh wait, I just looked it up and for longer/bigger numbers, they are divisible by 8 if the last three digits form a number that is divisible by 8. Hmmm...not sure how useful that is. 7's rule also doesn't look particularly useful. If you double the last digit and subtract it from the larger number, if that number is divisble by 7 than so is the complete number. I think the lack of usefulness of these rules is why they weren't included in my GRE study guide.
• An interger can be divided by 9 if the sum of its digits can be divided by 9.
• An interger can be divided by 10 if the units digit (the last digit of the number) is 0.
• An interger can be divided by 11 (this one is complicated) if you add the odd digits and add the even digits to get two values, then subtract them, and the difference is an interger that is divisible by 11.
• An interger can be divided by 12 if it can also be divided by both 3 and 4.

Example by yours truly (please use the rules yourself and check my work):

549,810,653 (a totally random number)

• Not divisible by 2 because the last digit is a 3 which is not divisible by 2
• Not divisible by 3 because the sum of the digits, 41 if I added correctly, is not divisible by 3.
• Not divisible by 4 because the last two digits form a number, 53, which is not divisible by 4
• Not divisible by 5 because the last digit is not 0 or 5.
• Not divisible by 6 because it is not divisible by either 2 or 3.
• Unsure about 7 and 8.
• Not divisible by 9 because the sum of the digits, 41 if I added correctly, is not divisible by 9.
• Not divisible by 10 because the last digit is not a 0.
• Not divisible by 11 because 24-17 (if I did those sums correctly) is 7, which is not divisible by 11.
• Not divisible by 12 because it is also not divisible by 3 and 4.

It looks like 549,810,653 might just be a prime number. What do you think?

Edited 10/12/09: I found a handy prime number calculator online, and learned 549, 810, 653 is not prime...it is divisible by 7. Ah, one of my blind spots.