C Power of 3 Program

What Is a Power of 3?

A positive integer is a power of 3 when it equals 3k for some integer k ≥ 0.

Powers of 3: 1, 3, 9, 27, 81, 243, ...

  1 = 3⁰
  3 = 3¹
  9 = 3²
 27 = 3³

Not: 0, 2, 6, 12, 18, negatives

How to Check a Power of 3 in C

Four clear steps — then pick a divide-down loop or a multiply-up loop.

1. Require n > 0.
2. While n is divisible by 3, set n = n / 3.
3. If the remaining value is 1, it was a power of three.
4. Or start at 1 and multiply by 3 until you match or pass n.

Pseudocode

function IsPowerOfThree(n):
    if n <= 0: return false

    while n % 3 == 0:
        n = n / 3

    return n == 1

Cheat Sheet

Keep these facts handy while writing the program.

Live Preview

Enter an integer to see each divide-by-3 step and the final verdict.

n = 27
Steps: 27 → 9 → 3 → 1
27 is a power of 3

Worked Walkthrough — n = 27

Divide by 3 whenever the remainder is zero; stop when you cannot.

27 % 3 == 0 → 27 / 3 = 9
 9 % 3 == 0 →  9 / 3 = 3
 3 % 3 == 0 →  3 / 3 = 1

1 % 3 != 0 → stop
remaining == 1 → power of 3

Counterexample n = 12:
  12 / 3 = 4
  4 % 3 != 0 → stop at 4 ≠ 1 → not a power of 3

C Programs

Start with the divide loop — it is the clearest exact check. Use the multiply-up loop when you want to show the sequence growing.

#include <stdio.h>

int is_power_of_three(int n)
{
    if (n <= 0)
        return 0;

    while (n % 3 == 0)
        n /= 3;

    return n == 1;
}

int main(void)
{
    int number = 27;

    if (is_power_of_three(number))
        printf("%d is a power of 3\n", number);
    else
        printf("%d is not a power of 3\n", number);

    return 0;
}

27 is a power of 3

#include <stdio.h>

int is_power_of_three(int n)
{
    long power;

    if (n <= 0)
        return 0;

    power = 1;
    while (power < n)
        power *= 3;

    return power == n;
}

int main(void)
{
    printf("%d\n", is_power_of_three(1));  /* 1 */
    printf("%d\n", is_power_of_three(27)); /* 1 */
    printf("%d\n", is_power_of_three(12)); /* 0 */
    printf("%d\n", is_power_of_three(0));  /* 0 */
    return 0;
}

1
1
0
0

Time and Space Complexity

Each step multiplies or divides by 3, so the number of iterations is proportional to the exponent.

Key Takeaways