A number is divisible by another number if it can be divided by that number without leaving a remainder. This means the division results in a whole number. In other words, the result is an integer, and there's no fractional part.
Understanding Divisibility
Divisibility is a fundamental concept in mathematics. It signifies that one number completely contains another. For example:
- Divisible: 12 is divisible by 3 because 12 / 3 = 4 (a whole number).
- Not Divisible: 13 is not divisible by 3 because 13 / 3 = 4 with a remainder of 1.
Several methods exist to determine divisibility without performing the full division. These are called divisibility rules. These rules exploit patterns in numbers to quickly check for divisibility by certain numbers. Examples include:
- Divisibility by 2: A number is divisible by 2 if its last digit is even (0, 2, 4, 6, or 8).
- Divisibility by 3: A number is divisible by 3 if the sum of its digits is divisible by 3.
- Divisibility by 5: A number is divisible by 5 if its last digit is 0 or 5.
More complex divisibility rules exist for larger numbers (See Divisibility Rules from 1 to 13).
Practical Application & Methods
In programming, the modulo operator (%) is commonly used to check divisibility. The modulo operator gives the remainder of a division. If the remainder is 0, the number is divisible. For example, in Python:
def is_divisible(number, divisor):
return number % divisor == 0
print(is_divisible(12, 3)) # Output: True
print(is_divisible(13, 3)) # Output: FalseSpreadsheets also provide functions for this. For instance, in Excel, the MOD function can be used similarly: =MOD(number, divisor)=0.
As stated in several sources: "A number is divisible by another number if it can be divided equally by that number; that is, if it yields a whole number when divided by that number." (SparkNotes). "Divisibility means that a number goes evenly (with no remainder) into a number."
