The number 72144
72144 is a composite number with 40 divisors. Its prime factorisation is × × 167. Divisors (40): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72 … 72144.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 72144: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.
- 2
72144 is composite. Its prime factorisation is
- 3
The divisors add up to 208320; without 72144 itself that is 136176, so 72144 is abundant (136176 is more than 72144). Euler's totient φ(72144) = 23904 numbers up to 72144 share no factor with it.
- 4
The digits of 72144 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 143 steps to reach 1.
LaTeX source of the formulas on this page
\[ 72144 = 2^{4} \times 3^{3} \times 167 \]72144 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 40 |
| Sum of divisors | 208320 |
| Euler totient φ(n) | 23904 |
| Square | 5204756736 |
| Cube | 375491969961984 |
| Square root | 268.596351 (= 12√501) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 143 |
| Scientific notation | 7.2144 × |
72144 in other forms
| Form | Value |
|---|---|
| In words | seventy-two thousand one hundred and forty-four |
| Binary (base 2) | 10001100111010000 |
| Octal (base 8) | 214720 |
| Hexadecimal (base 16) | 119D0 |
| Base 3 | 10122222000 |
| As time | 72144 seconds = 20 h 2 min 24 s |
Is 72144 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (72144 ÷ 2 = 36072) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (72144 ÷ 3 = 24048) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (72144 ÷ 4 = 18036) | 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 (72144 ÷ 6 = 12024) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 | Yes (72144 ÷ 8 = 9018) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (72144 ÷ 9 = 8016) | 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 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (72144 ÷ 12 = 6012) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 72144 a prime number?
No. 72144 = × × 167, so it is divisible by 2.
What are the factors of 72144?
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 108, 144, 167, 216, 334, 432, 501, 668, 1002, 1336, 1503, 2004, 2672, 3006, 4008, 4509, 6012, 8016, 9018, 12024, 18036, 24048, 36072, 72144.
What is 72144 in binary?
10001100111010000 (hexadecimal 119D0, octal 214720).
What is the square root of 72144?
About 268.5964, exactly 12√501.
Is 72144 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 72144?
72144 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.