The number 37401
37401 is a triangular number: 1 + 2 + … + 273 = 37401. Its prime factorisation is 3 × 7 × 13 × 137. Divisors (16): 1, 3, 7, 13, 21, 39, 91, 137, 273, 411, 959, 1781, 2877, 5343, 12467, 37401.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 37401: a triangular number: 1 + 2 + … + 273 = 37401.
- 2
37401 is composite. Its prime factorisation is
- 3
The divisors add up to 61824; without 37401 itself that is 24423, so 37401 is deficient (24423 is less than 37401). Euler's totient φ(37401) = 19584 numbers up to 37401 share no factor with it.
- 4
The digits of 37401 add up to 15, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 111 steps to reach 1.
LaTeX source of the formulas on this page
\[ 37401 = 3 \times 7 \times 13 \times 137 \]
37401 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 61824 |
| Euler totient φ(n) | 19584 |
| Square | 1398834801 |
| Cube | 52317820392201 |
| Square root | 193.393381 |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 111 |
| Scientific notation | 3.7401 × |
37401 in other forms
| Form | Value |
|---|---|
| In words | thirty-seven thousand four hundred and one |
| Binary (base 2) | 1001001000011001 |
| Octal (base 8) | 111031 |
| Hexadecimal (base 16) | 9219 |
| Base 3 | 1220022020 |
| As time | 37401 seconds = 10 h 23 min 21 s |
Is 37401 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | No (remainder 1) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (37401 ÷ 3 = 12467) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 1) | 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 | No (remainder 3) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (37401 ÷ 7 = 5343) | 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 1) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 1) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 9) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 37401 a prime number?
No. 37401 = 3 × 7 × 13 × 137, so it is divisible by 3.
What are the factors of 37401?
1, 3, 7, 13, 21, 39, 91, 137, 273, 411, 959, 1781, 2877, 5343, 12467, 37401.
What is 37401 in binary?
1001001000011001 (hexadecimal 9219, octal 111031).
What is the square root of 37401?
About 193.3934.
Is 37401 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 37401?
37401 is a triangular number: 1 + 2 + … + 273 = 37401.