Learning Some more Divisibility Rules Video Lecture - Advance Learner Course

hello friends this video are playing
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based on these concept of common factors
and multiples we will talk about some
additional divisibility rules so let us
quickly look at some additional
divisibility rules if a number is
divisible by another number it is also
divisible by each of its factors now let
us understand each of these with
examples now let us say we consider a
number 248 now we say that 248 is
divisible by 8 now we have found it by
actual division that it is divisible by
8 so as per this rule that this number
will become divisible by all the factors
of 8 now what are the factors of 8 so
factors of 8 would be 1 2 4 & 8 now if
we say that 248 is divisible by 8 that
by default means that 248 will be
divisible by 1 2 4 & 8 also so if a
number is divisible by a particular
number then the number will also be
divisible by all the factors of that
particular number next rule if a number
is divisible by 2 Oh prime numbers then
it is divisible by their product also
now this is interesting now let us take
the example of 18 now 18 is divisible by
2 yes we know that 18 is also divisible
by 3 right and 2 & 3 & Co prime numbers
why are the co prime because they have
only one common factor and that is 1 so
that is why they are Co prime numbers so
as per this rule if 18 is divisible by 2
18 is also divisible by 3 such that 2 &
3 are co-prime numbers then 18 will also
be divisible by product of the
prime numbers that means this would mean
that 18 is divisible by six which is the
product of these two prime numbers so
let us take another example it is
considered a number 100
so hundred is divisible by four hundred
is also divisible by five
and what about four and five do you
think they are co-prime numbers yes
because they have only one common factor
and that is 1 so therefore 100 will also
be divisible by product of 4 and 5 that
is 20 so hundred will be divisible by 20
Lex true if two given numbers are
divisible by a number then their sum is
also divisible by that number so let us
say that we have a number 16 now 16 is
divisible by 8 we have another number
say 32 and 32 is also divisible by 8 so
we have 2 different numbers which are
divisible by a same number now as per
this rule then the sum of these two
numbers would also be divisible by 8
that means the sum of 32 and 16 which is
equal to 48 then 48 will also be
divisible by 8 so you see these are some
very interesting rules of divisibility
because with these rules you can very
quickly decide whether a particular
number will be divisible by another
number or not because there now we have
told you the divisibility rules from
number two till number 12
now you might ask that how do I know if
a number is divisible by 12 or not if a
number is divisible by 24 or not so
those are the places where these rules
will be useful so let's say you want to
find out
the number will be divisible by 24 or
not so find out if the number is
divisible by the factors of 24 so that
is you know you'll be able to decide
whether a number is divisible by a
particular number rule number four if
two given numbers are divisible by a
number then their difference is also
divisible by that number so again let us
take an example it says 16 is divisible
by 8 we take some other number now let's
say 56 is also divisible by 8 so now
when you look at the difference between
56 and 16 which is equal to 40 so this
40 is also divisible by 8 so if two
numbers are divisible by a particular
number then the sum of those numbers is
also divisible the difference of those
two numbers is also divisible by 8 thank
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