Divisor vs Dividend
Addition, subtraction, multiplication and division are the four basic arithmetic operations done in the set of real numbers. Division is the inverse operation of multiplication. For example, [latex]2\\times 3 = 6 [/latex] and therefore, [latex]6\\div 3 = 2[/latex] . Unlike the other three operations, division is not closed in the set of integers. For example, [latex]3\\div 6 = \\frac{1}{2}[/latex] is not an integer. In other words, sometimes a remainder is left when a number is divided by another. To make the operation of division complete, the number system is extended from the set of integers to the set of rational numbers.
In the set of integers, the division algorithm plays a major role as far as division is concerned. It says that for each integer a, b (≠0), there exist unique integers q and r such that a = bq + r, where 0 ≤ q ≤ |b|. For example, taking a = 5 and b = 2, the unique values of q and r are 2 and 1 respectively, as 5 = 2*2 + 1. This shows that when 5 is divided by 2 in the set of integers, the answer is 2 and a remainder of 1 is left.
But in the set of real numbers the division there is no remainder. Let a, b (≠0) be two real numbers, then [latex]a\\div b = c [/latex] if and only if [latex]b = ac [/latex]
What is a divisor?
Consider the number b dividing the number a, i.e. [latex]b\\div a [/latex] . The number a is divided by the number b. Since, number b is the number by which another number is divided, it is called the divisor – the doer of the division. For example consider the case of dividing 5 by 2. Then, the divisor is 2. A very important thing to note about the divisor is that it is non-zero. It is because division by 0 is not-defined.
What is a dividend?
Consider the example in the previous example. There, a is the number which is divided by b – the divisor. The number a which is going to be divided is called the dividend. In the example of 5 being divided by 2, 5 is the dividend.
Thus, in the division algorithm, a is the dividend and b is the divisor.
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What is the difference between divisor and dividend? • Dividend is the number which is divided. The number from which the dividend is divided is called the divisor. • Dividend can be any real value whereas divisor should be non-zero.
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