The number 2401
2401 is a perfect power () and a perfect square (49²). Its prime factorisation is . Divisors (5): 1, 7, 49, 343, 2401.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 2401: a perfect power (); a perfect square (49²); a Harshad number: divisible by its digit sum 7.
- 2
2401 is composite. Its prime factorisation is
- 3
The divisors add up to 2801; without 2401 itself that is 400, so 2401 is deficient (400 is less than 2401). Euler's totient φ(2401) = 2058 numbers up to 2401 share no factor with it.
- 4
The digits of 2401 add up to 7, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 164 steps to reach 1.
LaTeX source of the formulas on this page
\[ 2401 = 7^{4} \]2401 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 5 |
| Sum of divisors | 2801 |
| Euler totient φ(n) | 2058 |
| Square | 5764801 |
| Cube | 13841287201 |
| Square root | 49 |
| Digit sum / digital root | 7 / 7 |
| Collatz steps to 1 | 164 |
| Scientific notation | 2.401 × |
| Perfect power |
2401 in other forms
| Form | Value |
|---|---|
| In words | two thousand four hundred and one |
| Roman numerals | MMCDI |
| Binary (base 2) | 100101100001 |
| Octal (base 8) | 4541 |
| Hexadecimal (base 16) | 961 |
| Base 3 | 10021221 |
| As time | 2401 seconds = 40 min 1 s |
Is 2401 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 | No (remainder 1) | 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 1) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (2401 ÷ 7 = 343) | 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 7) | 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 3) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 1) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 2401 a prime number?
No. 2401 = , so it is divisible by 7.
What are the factors of 2401?
1, 7, 49, 343, 2401.
What is 2401 in binary?
100101100001 (hexadecimal 961, octal 4541).
What is the square root of 2401?
49, because 49 × 49 = 2401.
What is 2401 in Roman numerals?
MMCDI.
Is 2401 divisible by 3?
No. Its digits add up to 7, which is not a multiple of 3.
What is special about the number 2401?
2401 is a perfect power (); a perfect square (49²); a Harshad number: divisible by its digit sum 7.