Consecutive numbers:
Consecutive numbers are numbers that follow each other in order without any gaps, where each number is exactly \(1\) more than the previous number. For example: \(5, 6, 7, 8\) are consecutive numbers.
General form of consecutive numbers:
Any consecutive number can be written as \(x\), (\(x + 1\)), (\(x + 2\)), (\(x + 3\)), ....
Any even consecutive number can be written as \(2x\), \(2x + 2\), \(2x + 4\), ....
Any odd consecutive number can be written as \(3x\), \(3x + 1\), \(3x + 3\), ....
Divisibility by \(2\):
Divisibility by \(2\): If the number ends at \(2\), \(4\), \(6\), \(8\) or \(0\), it is divisible by \(2\).
Divisibility by \(2\) means checking if a number is even. Parity is the mathematical word for whether a number is even or odd. If a number is even, its parity is even, and if it is odd, its parity is odd.
What is Parity?
Parity tells us if a number is even or odd:
- An even number leaves no remainder when divided by \(2\). It is called as even parity (eg: \(6 \div 2 = 3\) with remainder \(0\)).
- An odd number leaves a remainder of \(1\) when divided by \(2\). It is called as odd parity (eg: \(7 \div 2 = 3\) with remainder \(1\)).
Addition and Subtraction Parity:
odd \(\pm\) odd \(=\) even
even \(\pm\) even \(=\) even
odd \(\pm\) even \(=\) odd
Product of Parity:
odd \(\times\) even \(=\) even
odd \(\times\) odd \(=\) odd
Exponent Parity:
odd \(^3 =\) odd