Parity (Even/Odd) Math Example 4

Follow the full solution, then compare it with the other examples linked below.

Example 4

easy
Classify each as odd or even without fully computing: (a) 100+201100 + 201, (b) 6×7×86 \times 7 \times 8, (c) 15215^2.

Solution

  1. 1
    (a) 100100 even, 201201 odd: even + odd = odd.
  2. 2
    (b) 66 is even, so the product 6×7×86 \times 7 \times 8 is even (any factor even makes the product even).
  3. 3
    (c) 1515 is odd: odd ×\times odd = odd, so 15215^2 is odd.

Answer

(a) odd; (b) even; (c) odd.
Parity rules cascade through products and sums. A single even factor makes the whole product even. Powers of an odd number stay odd; powers of an even number stay even. These shortcuts avoid full computation.

About Parity (Even/Odd)

The classification of integers as even (evenly divisible by 2, with no remainder) or odd (not divisible by 2).

Learn more about Parity (Even/Odd) →

More Parity (Even/Odd) Examples

Example 1 easy

Without fully computing, determine the parity (odd or even) of [formula] and of [formula].

Example 2 medium

Prove that the sum of any two consecutive integers is always odd.

Example 3 medium

Prove that the sum of two odd numbers is always even.

Example 5 medium

In a group of [formula] people, each person shakes hands with every other person exactly once. Is th

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