The phrase "divisible by" refers to the mathematical property of a number being evenly divided or divisible by another number without any remainder. When one number is divisible by another, it implies that the quotient resulting from the division operation is a whole number.
To elaborate further, given two numbers, say 'a' and 'b', where 'b' is not equal to zero, we say that 'a' is divisible by 'b' if 'a' can be expressed as the product of 'b' and some whole number 'n', where 'n' can be any positive or negative integer or zero. In this context, 'a' is referred to as the dividend, 'b' as the divisor, and 'n' as the quotient.
For instance, if 'a' is divisible by 'b', we write it as 'a/b' or 'a ÷ b' using the division symbol. In this case, the remainder should be zero for the division operation to be considered exact.
For example, if we have a number 'a' that is divisible by 3, it means that 'a' can be expressed as the product of 3 and some integer 'n'. Consequently, if we divide 'a' by 3, the remainder will be zero.
Understanding divisibility is essential for various mathematical operations, including prime factorization, simplifying fractions, and determining common multiples or factors. It also finds applications across multiple domains, including arithmetic, algebra, number theory, and other areas of mathematics.
