The number 73152
73152 is a composite number with 42 divisors. Its prime factorisation is × × 127. Divisors (42): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72 … 73152.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 73152: a Harshad number: divisible by its digit sum 18.
- 2
73152 is composite. Its prime factorisation is
- 3
The divisors add up to 211328; without 73152 itself that is 138176, so 73152 is abundant (138176 is more than 73152). Euler's totient φ(73152) = 24192 numbers up to 73152 share no factor with it.
- 4
The digits of 73152 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 37 steps to reach 1.
LaTeX source of the formulas on this page
\[ 73152 = 2^{6} \times 3^{2} \times 127 \]73152 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 42 |
| Sum of divisors | 211328 |
| Euler totient φ(n) | 24192 |
| Square | 5351215104 |
| Cube | 391452087287808 |
| Square root | 270.466264 (= 24√127) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 37 |
| Scientific notation | 7.3152 × |
73152 in other forms
| Form | Value |
|---|---|
| In words | seventy-three thousand one hundred and fifty-two |
| Binary (base 2) | 10001110111000000 |
| Octal (base 8) | 216700 |
| Hexadecimal (base 16) | 11DC0 |
| Base 3 | 10201100100 |
| As time | 73152 seconds = 20 h 19 min 12 s |
Is 73152 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (73152 ÷ 2 = 36576) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (73152 ÷ 3 = 24384) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (73152 ÷ 4 = 18288) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 2) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (73152 ÷ 6 = 12192) | 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 (73152 ÷ 8 = 9144) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (73152 ÷ 9 = 8128) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 2) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 2) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (73152 ÷ 12 = 6096) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 73152 a prime number?
No. 73152 = × × 127, so it is divisible by 2.
What are the factors of 73152?
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 127, 144, 192, 254, 288, 381, 508, 576, 762, 1016, 1143, 1524, 2032, 2286, 3048, 4064, 4572, 6096, 8128, 9144, 12192, 18288, 24384, 36576, 73152.
What is 73152 in binary?
10001110111000000 (hexadecimal 11DC0, octal 216700).
What is the square root of 73152?
About 270.4663, exactly 24√127.
Is 73152 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 73152?
73152 is a Harshad number: divisible by its digit sum 18.