let's look at divisibility by the

numbers three six and nine first we look

at divisibility by three a number is

divisible by three if the sum of its

digits is divisible by three is twenty

five thousand seven hundred twenty two

divisible by three this number has five

digits let's add them two plus five plus

seven plus two plus two 2 plus 5 is 7 7

plus 7 is 14 and 14 plus four is 18 so

the sum of its digits is 18 is this sum

divisible by three yes 18 is divisible

by three hence this number is also

divisible by three if the sum is not

divisible by three then the number two

is not divisible by three let's zoom out

and understand another divisibility rule

divisibility by 6 is not the simplest

but it's definitely very interesting

there are just two simple conditions we

can say that a number is divisible by 6

if the number is even and is divisible

by 3 both these conditions have to be

satisfied it has to be even and it has

to be divisible by 3 since the test is a

bit different we will look at two

examples the first one is four hundred

and seventy nine thousand six hundred

twenty-three is this number even since

the last digit is not divisible by two

this number is not divisible by two

hence this number is not even so we

don't need to check for the other

condition here even if one of them is

not satisfied the number will not be

divisible by six here it's not even and

hence will not be divisible by six

consider one hundred and ninety thousand

one hundred sixteen this number is

divisible by two as the last digit

divisible by two hence it's even the

first condition is satisfied now we

check for the second condition we check

if it is divisible by three a number is

divisible by three if this sum of its

digits is divisible by three so we find

out the sum of the digits one plus nine

plus zero plus one plus one plus six

one plus 9 is 10 plus 2 is 12 plus 6

gives us 18 the sum equals 18 so it is

also divisible by three

hence this number is divisible by six

now we come to the final divisibility

test of this video the test for

divisibility by nine is similar to that

of the test for divisibility by three a

number is divisible by nine if the sum

of its digits is divisible by nine is

two million four hundred and seventy

nine thousand four hundred and one

divisible by nine the sum of the digits

equals 27 since 27 is divisible by nine

this number will also be divisible by

nine

you