Learn about Divisibility by 2, 3, 5, 9, or 10 In this track let’s learn about divisibility of numbers by 2, 3, 4, 9, and 10. The question asks us to check of the number 230 is divisible by the numbers 2, 3, 5, 9 or 10, first we need to know that a number is divisible by another number if when I divide the first number the division gives a whole number and no remainder. The key is no remainder. What we’re going to learn in this track are tricks on how to do it faster, so first is divisibility by 2, so we have to check if 230 is divisible by 2. Here’s the trick, in order to check if a number is divisible by 2, the last digit should be an even number. That’s the key to remember is the last number an even number, so in the case of 230 the last digit is 0, is 0 an even number? Yes, so this is divisible by 2 rights, I don’t even have to divide it. Second, lets look at divisibility by 3, so when I look at divisibility by 3 in a number like 230 first the trick that I have to remember, if it is divisible by 3, the check that I have to do is look at the sum of all digits divisible by 3, that’s the key to remember. Sum of all digits should be divisible by 3, so in this case is the number 230, the sum of all digits is 2 + 3 + 0 is 5. Is 5 divisible by 3? 5 divided by 3 will give me 1 and will leave me a number, so that is no, so that means that the answer to this is no. I don’t even have to do the division; I can just apply the trick that says if the sum of all digits is divisible by 3 in this case is no, so the entire number is not divisible by 3. Now the next is by 5, so I have to check if 230 is divisible by 5, okay? The trick here is for a number to be divisible by 5, the last digit should be 5 or 0, that’s the only time it can be divisible by 5. So in this example is 230, the last digit is this one, it's 0 which is part of the condition so the answer is yes, 230 is divisible by 5 because the last digit is 5 or 0, in this case it's 0. The divisibility check for 9 is 230 is divisible by 9 if the sum of all digits is divisible by 9. In this case the sum of all digits is 2 + 3 + 0 = 5, 5 is not divisible by 9 is not a whole number so the answer is no. So the sum of all digits is not divisible by 9, the number is not divisible by 9 so 230 would not be divisible by 9. Now the last question is divisibility by 10, this is a simple 10, for 230 to be divisible by 10 the last digit should be 0, in this case the last digit is indeed 0 so is the number divisible by 10? The answer is yes, so what have we learned, quickly to recap what we’ve learned is there are short cuts we can apply to determine if a number is divisible by numbers like 2, 3, 5 9 or 10. If a number is divisible by 2 it's last digit will be an even number. Even numbers are 2, 4, 6, and 8, in this case because the last digit is 0 it will be divisible by 2. For a number to be divisible by 3, the sum of all digits should be divisible by 3, sum of all digits is 5 so the answer is no. For it to be divisible by 5 the last digit should be 5 or 0 which in this case is true. For it to be divisible by 9 the sum of all digits should be 9 which in this case is not true and for a number to be divisible by 10 the last digit should be 0 which in this case is indeed true. So these are short ways of figuring this out.