The number 37152
37152 is a composite number with 48 divisors. Its prime factorisation is × × 43. Divisors (48): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 43, 48 … 37152.
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How to work it out
- 1
What is special about 37152: a Harshad number: divisible by its digit sum 18.
- 2
37152 is composite. Its prime factorisation is
- 3
The divisors add up to 110880; without 37152 itself that is 73728, so 37152 is abundant (73728 is more than 37152). Euler's totient φ(37152) = 12096 numbers up to 37152 share no factor with it.
- 4
The digits of 37152 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 186 steps to reach 1.
LaTeX source of the formulas on this page
\[ 37152 = 2^{5} \times 3^{3} \times 43 \]37152 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 110880 |
| Euler totient φ(n) | 12096 |
| Square | 1380271104 |
| Cube | 51279832055808 |
| Square root | 192.748541 (= 12√258) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 186 |
| Scientific notation | 3.7152 × |
37152 in other forms
| Form | Value |
|---|---|
| In words | thirty-seven thousand one hundred and fifty-two |
| Binary (base 2) | 1001000100100000 |
| Octal (base 8) | 110440 |
| Hexadecimal (base 16) | 9120 |
| Base 3 | 1212222000 |
| As time | 37152 seconds = 10 h 19 min 12 s |
Is 37152 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (37152 ÷ 2 = 18576) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (37152 ÷ 3 = 12384) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (37152 ÷ 4 = 9288) | 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 (37152 ÷ 6 = 6192) | 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 | Yes (37152 ÷ 8 = 4644) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (37152 ÷ 9 = 4128) | 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 5) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (37152 ÷ 12 = 3096) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 37152 a prime number?
No. 37152 = × × 43, so it is divisible by 2.
What are the factors of 37152?
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 43, 48, 54, 72, 86, 96, 108, 129, 144, 172, 216, 258, 288, 344, 387, 432, 516, 688, 774, 864, 1032, 1161, 1376, 1548, 2064, 2322, 3096, 4128, 4644, 6192, 9288, 12384, 18576, 37152.
What is 37152 in binary?
1001000100100000 (hexadecimal 9120, octal 110440).
What is the square root of 37152?
About 192.7485, exactly 12√258.
Is 37152 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 37152?
37152 is a Harshad number: divisible by its digit sum 18.