 Okay friends. So in this session, let us start with a question. So the question is What would be the quotient if four six nine one two three is? divided divided by seven six five one Now I know the moment I would have uttered the word divided and you'd have got cold feet now You know, it's not only you it's you know me or including anyone in this world who has done arithmetic division division is The most dreaded of the four arithmetic operation namely addition add subtract Multiply multiply and Division so given a choice. We would always go for add then probably will go for subtraction and then multiplication and division in that order So in my opinion or whosoever I have encountered. I know division is the last set last Arithmetic operation in the priority list. Now. Why is this division so difficult? You know and why people are Not willing to take a plunge in arithmetic calculations including division So to answer this and to understand division in much more detailed way is this is dedication We are dedicating this session towards and that is what is What is? Divisibility Divisibility Okay, so this is the question which we are going to Answer today just for your information there, you know, you must have encountered Language like a and then this sign this sign divide by b. Do you know what this sign is this sign? This sign is called Obelisk, what is it called? Obelisk and you know, this is a Most common symbol for division which we have been using since our childhood and you know Who did you know? Who was the guy who introduced this sign into mathematics the name of the scientist or the mathematician was? he was a Swiss mathematician he was a Swiss mathematician and and his name was his name was Johan Johan ran He was and this guy introduced this obelisk symbol into mathematics in the year 1659 through his book called Toys algebra, so the it's spelled like t u e t u t e u sorry T s c h e toys algebra So in this book for the first time the symbol obelisk was used which we have been using So commonly for division now To come back to the topic of the session the session is dedicated towards to understand the question What is divisibility and to answer this we have to have our definition first and the definition goes like this Definition says and please mark the words which I am using a Non-zero, so please mark the words which I'm using a non-zero integer integer non-zero integer a a is is said said to divide to divide said to divide another another integer Another integer B and if you notice if you're not if would have noticed here. I have not used non-zero here It's any integer right so a but a non-zero integer a is said to divide another integer B if there exists If there exists integer Another integer C See again, I have not used non-zero, you know, so hence I'm trying to re-emphasize it again and again So a non-zero integer a is said to divide another integer B if there exists integer C such that such that B equals a times C Okay, so and a Would divide B if there exists an integer and only an integer when we get an integer only Here then we say that we have Then we say that a divides B. So this guy has to be an integer Let's take an example and stand Let's take an example and understand this so Example B Let me just add another Yeah, so if you see example would be let's say We say that five which is an is it a non-zero integer? Yes, it is a non-zero integer five non-zero integer Five divides 30 why because we can express 30 as five into six and six so hence if you see this is my B here. This is my a and This is C all of them are integers and a is clearly not equal to Zero right so hence we say five is a five divides 30 and how do I express? So, you know, how do I express divisibility? I say Five divides 30. So a vertical line between five and 30 means what does it mean? This means five is a Factor either this or let me start with this at five divides 30 or we say five is a factor factor of 30 or we say 30 is 30 is a multiple multiple of Five right because I have another integer six when my been multiplied with five It's called and we'll get 30. Okay. So another examples could be that let us take some other examples So clearly six divides 42 Why because 42 can be expressed as six into seven so if you see this number is my B This is clearly my a and this is See so C is an integer similarly I can say Eight divides minus 64 Yeah, so hence, you know if you have this doubt whether we can have a negative integer over here Yes, you can have so I can say minus 64 is equal to eight into Minus eight clearly. This is my a which is not equal to zero Not zero a is not equal to zero. This is what this is my C. It is minus eight is an integer So there's no restriction on whether it should be only positive or negative and this is clearly my B B right, so this is how we express Divisibility now clearly there are examples when let's say some number is not of not it doesn't divide any particular number So for example, let's say five doesn't divide. So I will write five doesn't divide 31 why because there exists because there exists no integer such that 31 is equal to five into let's say C now C is Not an integer here Because if you if you know the division if you if you see it it is 6.2, isn't it? So C here is 6.2 Right, but see this is not an integer not an integer. So hence we don't say hence we say five doesn't divide 31 similarly seven doesn't divide 20 similarly eight Doesn't divide 19 and so on and so forth Okay, so hope you understood what divisibility means and how do we express? Divisibility and in the next session we'll try and understand what are different properties of divisibility Thanks for watching this video