THE FUNDAMENTALS

Number basics.

Zero, negative numbers, very big integers. Start with the rules, then find the exceptions that aren’t exceptions.

12 guides

Number basics01

How to tell if a number is odd

Check an integer’s last digit, divide it by two, or write it as 2k + 1. Learn three exact methods with examples and input tips.

2 min read
Number basics02

What is an odd integer?

Understand the definition n = 2k + 1, including negative odd integers, equivalent formulas, and why integers cannot be both odd and even.

2 min read
Number basics03

Is zero odd or even?

Zero is even because 0 = 2 × 0. See the definition, the number-line pattern, and the difference between dividing zero and dividing by zero.

2 min read
Number basics04

Can negative numbers be odd?

Negative integers can be odd or even. Learn why sign does not change parity and why JavaScript’s negative remainder needs a careful test.

2 min read
Number basics05

Are decimals odd or even?

Non-integer decimals are neither odd nor even, but 3.0 is an odd integer value. Separate mathematical value from decimal notation and input syntax.

2 min read
Number basics06

Odd and even number rules

Predict parity for addition, subtraction, multiplication, and powers. See the algebra behind the rules and why division needs more information.

3 min read
Number basics07

The last-digit test for odd numbers

Learn why decimal integers ending in 1, 3, 5, 7, or 9 are odd, including the proof, negative numbers, leading zeros, and common traps.

2 min read
Number basics08

Modulo versus remainder when testing odd numbers

Understand why −7 modulo 2 is 1 while JavaScript returns −1 for -7 % 2, and write an odd-number test that handles both signs.

2 min read
Number basics09

Odd numbers in binary

An integer’s last binary digit determines whether its value is odd. Learn the place-value proof and avoid confusing value parity with bit-count parity.

2 min read
Number basics10

How to check the parity of a large integer

Keep large integers exact with digit strings or BigInt. Learn why converting 9007199254740993 to a JavaScript Number can reverse the answer.

2 min read
Number basics11

Odd numbers and prime numbers are different

All primes greater than two are odd, but many odd numbers are composite. Understand the distinction with examples, proofs, and the special case of one.

3 min read
Number basics12

Common odd-number mistakes and how to avoid them

Avoid the usual parity traps: zero, negative remainders, decimals, rounded integers, prime numbers, and confusing a number’s value with its spelling.

3 min read