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In math, a number is said to be divisible by another number if the remainder after division is 0. Learn the important divisibility rules along with examples.
Definition of Divisible. A number p p is divisible by a number q q if q q goes into p p an even number of times, without anything left over. For example, 18 18 is divisible by 3 3 because 18 ÷ 3 = 6 18 ÷ 3 = 6, with no remainder.
Use the definition of divisibility to show that given any integers \(a\), \(b\), and \(c\), where \(a\neq0\), if \(a\mid b\) and \(a\mid c\), then \(a\mid(sb^2+tc^2)\) for any integers \(s\) and \(t\).
Illustrated definition of Divisible: When dividing by a certain number gets a whole number answer. Example: 15 is divisible by 3, because...
Divisibility rules are a set of general rules that are often used to determine whether or not a number is absolutely divisible by another number. Note that “divisible by” means a number divides the given number without any remainder, and the answer is a whole number.
Definition. When a number gets completely divided by another number, without leaving any remainder, that number is said to be divisible by the other number. For example, 10 is completely divided by 2 and thus is divisible by 2 but it is not completely divided by 3 – leaving a remainder of 1 – and so is not divisible by 3.
Divisibility refers to the ability of one integer to be evenly divided by another without leaving a remainder. This concept is fundamental in number theory, as it forms the basis for various mathematical principles and proofs.
