The number 37206
37206 is a composite number with 32 divisors. Its prime factorisation is 2 × × 13 × 53. Divisors (32): 1, 2, 3, 6, 9, 13, 18, 26, 27, 39, 53, 54, 78, 106, 117, 159 … 37206.
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How to work it out
- 1
What is special about 37206: a Harshad number: divisible by its digit sum 18.
- 2
37206 is composite. Its prime factorisation is
- 3
The divisors add up to 90720; without 37206 itself that is 53514, so 37206 is abundant (53514 is more than 37206). Euler's totient φ(37206) = 11232 numbers up to 37206 share no factor with it.
- 4
The digits of 37206 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
\[ 37206 = 2 \times 3^{3} \times 13 \times 53 \]37206 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 90720 |
| Euler totient φ(n) | 11232 |
| Square | 1384286436 |
| Cube | 51503761137816 |
| Square root | 192.888569 (= 3√4134) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 186 |
| Scientific notation | 3.7206 × |
37206 in other forms
| Form | Value |
|---|---|
| In words | thirty-seven thousand two hundred and six |
| Binary (base 2) | 1001000101010110 |
| Octal (base 8) | 110526 |
| Hexadecimal (base 16) | 9156 |
| Base 3 | 1220001000 |
| As time | 37206 seconds = 10 h 20 min 6 s |
Is 37206 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (37206 ÷ 2 = 18603) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (37206 ÷ 3 = 12402) | 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 1) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (37206 ÷ 6 = 6201) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 1) | 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 (37206 ÷ 9 = 4134) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 6) | 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 37206 a prime number?
No. 37206 = 2 × × 13 × 53, so it is divisible by 2.
What are the factors of 37206?
1, 2, 3, 6, 9, 13, 18, 26, 27, 39, 53, 54, 78, 106, 117, 159, 234, 318, 351, 477, 689, 702, 954, 1378, 1431, 2067, 2862, 4134, 6201, 12402, 18603, 37206.
What is 37206 in binary?
1001000101010110 (hexadecimal 9156, octal 110526).
What is the square root of 37206?
About 192.8886, exactly 3√4134.
Is 37206 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 37206?
37206 is a Harshad number: divisible by its digit sum 18.