Today's soundtrack is Saor: Aura. I absolutely adore this atmospheric Celtic black metal album in its entirety.
I'm now on chapter 7 of Basic Math and Pre-Algebra for Dummies, which is titled "Divisibility." This chapter discusses finding out whether a number can be divided by another without a remainder, prime numbers, and composite numbers.
Divisibility Tricks
The book goes over some tricks to help identify remainderless divisibility. Every number is divisible by one and itself. No number is divisible by zero. Every even number is divisible by two. Every number that ends in 0 or 5 is divisible by five. Every number that ends in a 0 is divisible by ten; if it ends in 00, it is divisible by 100, and so on.
We can find out whether a number is divisible by 3, 9, or 11 by checking its digital root. We do so by adding the number's digits to each other, repeating as needed until we are at a single digit.
If a number's digital root is 3, 6, or 9, it is divisible by three. If a number's digital root is 9, it is divisible by nine.
Two-digit repeating numbers (22, 66) are always divisible by eleven. Three-digit numbers whose digital root equals the tens column of that number are divisible by eleven. For 4+ digit numbers, add alternating positive/negative symbols between the digits to find the digital root. If the sum equals 0, 11, or any other two-digit repeating number, or a three-digit number whose tens column is the same as its digital root, that 4+ digit number will be divisible by eleven.
Prime and Composite Numbers
A prime number is only divisible by 1 and the number itself. A composite number can be divided by at least one other number. Every number except 1 and 0 is either prime or composite.
Every composite number under 100 is divisible by 2, 3, 5, or 7.
