Divisibility tests
Divisibility Tests for 2, 3, 4, 5, 6, 9, 10 Worked example of basic divisibility tests
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- What we're going to do in this video are some real quick tests to see if
- these three random numbers are divisible by any of these numbers here
- now I'm not going to focus a lot on the "why" of why they're divisible
- but rather just to give you a sense of how do you actually test to see this is divisible by two
- or five or nine, or ten.
- so let's get started
- so to test whether any of these are really divisible by two,
- you really just gotta look at the ones place
- and see if the ones place is divisible by 2
- and right over here, it is divisible by two,
- so this thing is gonna be divisible by two
- Zero is considered to be divisible by two
- so this is going to be divisible by two.
- Another way to think about it is
- is if you have an even number over here,
- and Zero is considered an even number,
- then you're going to be divisible by two.
- So over here,
- Do not have a number that is divisible by two
- this is five, so this is not divisible by two
- so I won't write any two there.
- we've gone through the twos,
- now let's go through the threes.
- so to figure out if you are divisible by three,
- you really just have to add up the digits
- and figure out if the sum is divisible
- by three.
- Do that. So if I do 2 + 7 + 9
- actually let me just write it out. +9 + 5
- +8 +8. What's this going to be?
- 2 + 7 is 9, 9 + 9 is 18, + 9 is
- 27, + 5 is 32,
- + 8 is 40, + 8 is 48
- and 48 is divisible by three,
- but in case you're not sure,
- since this is equal to 48, in case you're not sure
- whether this is divisible by 3,
- you can just add these digits up again.
- So 4 + 8
- is equal to 12, and 12 clearly
- is divisible by 3.
- And if you're not even sure there,
- you can add those digits up.
- 1 + 2 is equal to 3.
- So this is divisible by 3.
- This right over here, let's add up the digits!
- 5 + 6 = 11
- 11 + 7 = 18, + 0 is 18
- and if you want to add the 1 + 8 in 18,
- you get 9
- so the digits add up to 9.
- So these add up to nine.
- They add to 18, which is clearly divisible by 3,
- and these two things will add up to 9.
- So the important thing to know, is that when you add up all the digits, the sum
- is divisible by three
- So this is divisible by three, as well.
- Let's add up these digits.
- 1 + 0 + 0 + 7 =8, + 6 = 14
- + 5 = 19
- So 19 is not
- divisible by 3. So this one we're not gonna write a three by there.
- It's not divisible by 3.
- Let's try 4.
- Think about four, you just have to think about the last 2 digits,
- To see are the last 2 digits
- divisible by four.
- Immediately, you could look at this one over here,
- see it's an odd number,
- if it's not divisible by 2, it's definitely not going to be
- divisible by four.
- This one is not divisible by any of the first four numbers
- 88. Is that divisible by 4?
- You can do that in your head. That's 4 x 22!
- So this is divisible by 4.
- Now let's see, 4 goes into 60 15 times
- and then to go from 60 to 70 you have to go another 10,
- so it's not divisible by four.
- You could even try to divide it out yourself.
- Four goes into 70, 1 time, subtract get 30,
- 7 times, multiply, subtract, get a 2 over here as your remainder.
- So it is not divisible by 4,
- Now let's move on to five.
- And you are probably already very familiar with this,
- if your final digit is a 5 or 0, you are divisible by five.
- So this one's not divisible by 5.
- This one is divisible by 5.
- And this you have a 5, as your ones digit, so finally this is divisible by something,
- it's divisible by 5.
- Now the number 6. The simple way to think about divisibility by 6
- is that you have to be divisible by both 2 and 3,
- to be divisible by 6, because
- the prime factorization of 6 is
- 2 times 3. So here we're divisible by 2 and 3, so
- we're going to be divisible by 6.
- Here we're divisible by 2 and 3, so we're divisible by 6!
- And if you were just divisible by only a 2
- or a 3, you wouldn't be able to do this
- you have to have both 2 and 3
- and here you're divisible by neither 2 or 3,
- so you're not going to be divisible by 6.
- Now let's do the test for 9.
- The test for 9 is very similar to the test for 3
- Sum up all the digits. If the sum is divisible by 9,
- then you're there.
- We already summed up the digits here,
- 48 is not divisible by 9,
- if you're not sure, you can add up the digits there and get 12,
- 12 is definitely not divisible by 9.
- So this thing right over here is not divisible by 9.
- This one over here we added up all the digits and got 18,
- 18 is divisible by 9.
- So this one is divisible by 9.
- And this one over here, you don't even have to add them up,
- because we already know it's not divisible by 3,
- if it's not divisible by 3, it can't be divisible by 9
- but if you did add up the digits, you'd get 19
- which is not divisible by 9.
- So this also is not divisible by 9.
- And finally, divisibility by 10.
- And this is the easiest one of all.
- Cause you just have to see if you have a zero
- in the ones place.
- You clearly do not have a zero in the ones place here.
- You do have a zero in the ones place here.
- So you are divisible by 10 here,
- are then finally you don't have a zero in the ones place
- here, so you're not going to be divisible by 10.
- Another way you could think about it,
- you have to be divisible by both 2 and 5
- to be divisible by 10.
- Here you are divisible by 5, but not 2.
- Obviously the easiest way is just to see if you have
- a zero in the ones place.
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