Is Even

Purpose

Provide a clear, repeatable template for determining whether a number is even or odd. Use consistent variable names in explanations: n , remainder , is_even .

Quick Rules

• Even numbers are divisible by 2 with no remainder.

• Odd numbers have a remainder of 1 when divided by 2.

• Parity applies to integers; for non-integers, state that even/odd is undefined unless the user asks to round.

Determining Evenness Template

Use this structure when responding:

Input: <value> Normalized integer (n): <integer or "not an integer"> Calculation: remainder = n % 2 Decision: is_even = (remainder == 0) Result: <even|odd|not applicable> Rationale: <short explanation>

Normalization Notes

• If the input is a numeric string, parse it to an integer and proceed.

• If the input is a decimal or non-numeric, state that even/odd does not apply.

• For negative integers, use the same modulo rule (sign does not change parity).

Example Responses

Example A (integer):

Input: 42 Normalized integer (n): 42 Calculation: remainder = 42 % 2 = 0 Decision: is_even = (remainder == 0) = true Result: even Rationale: 42 divides by 2 with no remainder.

Example B (non-integer):

Input: 3.14 Normalized integer (n): not an integer Calculation: remainder = n % 2 Decision: is_even = false Result: not applicable Rationale: Even/odd applies only to integers unless rounding is requested.

Example Set (69 total; 34 even, 35 odd)

Even examples:

• 0 -> even

• 2 -> even

• 4 -> even

• 6 -> even

• 8 -> even

• 10 -> even

• 12 -> even

• 14 -> even

• 16 -> even

• 18 -> even

• 20 -> even

• 22 -> even

• 24 -> even

• 26 -> even

• 28 -> even

• 30 -> even

• 32 -> even

• 34 -> even

• 36 -> even

• 38 -> even

• 40 -> even

• 42 -> even

• 44 -> even

• 46 -> even

• 48 -> even

• 50 -> even

• 52 -> even

• 54 -> even

• 56 -> even

• 58 -> even

• 60 -> even

• 62 -> even

• 64 -> even

• 66 -> even

Odd examples:

• 1 -> odd

• 3 -> odd

• 5 -> odd

• 7 -> odd

• 9 -> odd

• 11 -> odd

• 13 -> odd

• 15 -> odd

• 17 -> odd

• 19 -> odd

• 21 -> odd

• 23 -> odd

• 25 -> odd

• 27 -> odd

• 29 -> odd

• 31 -> odd

• 33 -> odd

• 35 -> odd

• 37 -> odd

• 39 -> odd

• 41 -> odd

• 43 -> odd

• 45 -> odd

• 47 -> odd

• 49 -> odd

• 51 -> odd

• 53 -> odd

• 55 -> odd

• 57 -> odd

• 59 -> odd

• 61 -> odd

• 63 -> odd

• 65 -> odd

• 67 -> odd

• 69 -> odd