Welcome to a lesson on divisibility rules. The goal of this video is to determine
if a given number is divisible by two, three, four, five, six,
eight, nine and ten. So let's go ahead and take a look at each rule.
A number is divisible by two
if it is even or ends in zero, two,
four, six or eight. So for example if we take a look at the number five hundred twelve,
and the number four hundred thirty-one.
We're only concerned about the last digit or the
digit in the ones place value. Five hundred twelve ends in two,
which means it's even and therefore is divisible by two.
However four hundred thirty-one ends in a
one, which means it's not even or that it's odd,
and it is not divisible by two. A number is divisible by four
if the last two digits are divisible by four.
If we take a look at six hundred twenty-four,
and six hundred twenty-one. Now we're only concerned about the last two digits here, the two and the four,
and here, the two and the one. Well, twenty-four
is divisible by four, and therefore so is six hundred twenty-four.
But for our second number,
twenty-one is not divisible by four, and therefore six hundred twenty-one
is not divisible by four. Next we'll take a look at the number eight.
A number is divisible by eight if the last three digits are divisible by
eight. Now I don't use this role very often because is often hard to tell
whether a three digit number is divisible by eight.
However if we did have a number, let's say five thousand
eighty-eight. The last three digits would be zero, eight, eight.
And since eighty-eight is divisible by eight, then so would five thousand eighty-eight.
Now let's take a look at the number three.
A number is divisible by three if the sum of the digits
is divisible by three. So for example if we compare
eight hundred thirteen and seven hundred twenty-four,
we need to sum these digits, which means we'll take
eight plus one, plus three.
That's going to give us twelve. And over here we'd have seven plus
two, plus four, that's going to give us thirteen.
So if this sum is divisible by three,
then so is the original number. And since twelve is divisible by three,
eight hundred thirteen is divisible by three.
However, over here we have thirteen.
Thirteen is not divisible by three and therefore seven hundred twenty-four is not visible by three.
Next, a number is divisible by six
if it is divisible by two and three.
So we already covered the rules for two and three. So let's go ahead and give it a
try.
Using the numbers three hundred seventy-two,
and three hundred sixty-two.
Now what we have to do here is use the divisibility rules for two and three for
both of these numbers.
Notice that both of these numbers end in two,
and therefore are divisible by two. But we also have the check divisibility by
three.
So what we do now is sum these digits. Well, three plus
seven, plus two, that gives us twelve. Twelve is divisible by three,
therefore three hundred seventy-two is divisible by three,
so three hundred seventy-two is also divisible by six.
However, over here three plus
six, plus two, that would be equal to eleven.
Eleven is not divisible by three,
and therefore three hundred sixty-two is not divisible by three
or divisible by six. For the number nine,
a number is divisible by nine if the sum of the digits
is divisible by nine as well. So if we take a look at six hundred thirty-nine,
and seven hundred twenty-six, we again need to find the sum of the digits.
Six plus three, plus nine, that would be eighteen.
And since eighteen is divisible by nine, so is six hundred thirty-nine.
Here the sum would be seven plus two, plus six,
that would be fifteen. Fifteen is not divisible by nine,
and therefore seven hundred twenty-six is not divisible by nine.
And we have two more rules to look at. A number is divisible by 10
if it ends in a zero. And this rule is pretty straightforward if we compare
five thousand, eight hundred twenty, and
five thousand, six hundred twenty-four.
This number ends in a zero or has a zero in the ones place value,
and therefore is divisible by ten.
Five thousand, six hundred twenty-four does not end in a zero,
and therefore is not divisible by ten.
And then the last row we're going to take a look at. A number is this a by five
if it ends in a zero or a five,
or it has a zero or a five in the ones place value.
So if we take a look at nine thousand, seven hundred eighty-five,
and six thousand, two hundred seventy-six.
This number here is divisible by five because it ends in a five or a zero,
and this number here is not divisible by five because it does not
end in a zero or five.
Now let's go ahead and take a look at a couple more problems. Here we want to determine if the given
numbers are divisible by two, three, four, five, six,
eight, nine and ten. So now we'll go through all these rules for an individual number.
Let's go ahead and list these possible divisors.
The rule for two, is it has to be an even number
or ends in a zero two, four, six or eight. And it does it end in a four,
so it is divisible by two.
To determine if its divisible by three, we have to sum these digits.
Well, eight plus zero, plus six, plus four,
that would give us eighteen. Eighteen is divisible by
three, and therefore so is the given number.
And remember if a number is divisible by two and three,
it's also divisible by six. We can go ahead and circle six.
To determine if it's divisible by four, we have to take a look at the last two
digits
which would be six and four, or sixty-four.
And since sixty-four is divisible by four,
so is the given number. For five it has to end in a zero or five, which it
doesn't,
so it's not divisible by five.
To determine if it's divisible by eight, if we take a look at the last three digits or zero, six, four.
Well, since sixty-four is divisible by eight,
so is the given number. To test for nine, we have to find the sum of the digits,
which we already did, to determine if it was divisible by three.
The sum of the digits is eighteen. Eighteen is divisible by nine,
therefore, so is the given number. And then for ten it has to end in a zero,
which it doesn't. Therefore it's not
divisible by ten. So it's divisible by two, three, four, six,
eight and nine. Let's go ahead and try one more. Let's take a look at two hundred seventy.
Let's go ahead and list the possible divisors again.
It ends in a zero and therefore is even,
so it's divisible by two.
And because it ends in a zero, we also know that it's divisible by ten,
as well as five. To determine if it's
divisible by three, we have to sum the digits. Two plus seven, plus
zero, that would be nine.
And since nine is divisible by three, so is the given number.
And since we have the sum of the digits, let's go and test for nine.
Since nine is divisible by nine, so is the given number.
To test for four, we take a look at the last two digits, that would give us
seventy. Seventy is not divisible by four,
and therefore the given number is not divisible by four.
To be divisible by six, it has to be divisible by two and three, which it is.
And then lastly, to test for eight, we have to take a look at the last three digits
which is the entire number, two hundred seventy.
This rule isn't very helpful and two hundred seventy
is not divisible by eight.
Okay, that's going to do it for this video. I hope you found it helpful.