The number 72054
72054 is a composite number with 12 divisors. Its prime factorisation is 2 × × 4003. Divisors (12): 1, 2, 3, 6, 9, 18, 4003, 8006, 12009, 24018, 36027, 72054.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 72054: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.
- 2
72054 is composite. Its prime factorisation is
- 3
The divisors add up to 156156; without 72054 itself that is 84102, so 72054 is abundant (84102 is more than 72054). Euler's totient φ(72054) = 24012 numbers up to 72054 share no factor with it.
- 4
The digits of 72054 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 68 steps to reach 1.
LaTeX source of the formulas on this page
\[ 72054 = 2 \times 3^{2} \times 4003 \]72054 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 156156 |
| Euler totient φ(n) | 24012 |
| Square | 5191778916 |
| Cube | 374088438013464 |
| Square root | 268.428761 (= 3√8006) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 68 |
| Scientific notation | 7.2054 × |
72054 in other forms
| Form | Value |
|---|---|
| In words | seventy-two thousand and fifty-four |
| Binary (base 2) | 10001100101110110 |
| Octal (base 8) | 214566 |
| Hexadecimal (base 16) | 11976 |
| Base 3 | 10122211200 |
| As time | 72054 seconds = 20 h 0 min 54 s |
Is 72054 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (72054 ÷ 2 = 36027) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (72054 ÷ 3 = 24018) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 2) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 4) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (72054 ÷ 6 = 12009) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | A number is divisible by 7 if double the last digit and subtract it from the rest: the result is a multiple of 7. |
| 8 | No (remainder 6) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (72054 ÷ 9 = 8006) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 4) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 6) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 72054 a prime number?
No. 72054 = 2 × × 4003, so it is divisible by 2.
What are the factors of 72054?
1, 2, 3, 6, 9, 18, 4003, 8006, 12009, 24018, 36027, 72054.
What is 72054 in binary?
10001100101110110 (hexadecimal 11976, octal 214566).
What is the square root of 72054?
About 268.4288, exactly 3√8006.
Is 72054 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 72054?
72054 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.