The number 400
400 is a perfect square (20²). Its prime factorisation is × . Divisors (15): 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 400: a perfect square (20²); a Harshad number: divisible by its digit sum 4.
- 2
400 is composite. Its prime factorisation is
- 3
The divisors add up to 961; without 400 itself that is 561, so 400 is abundant (561 is more than 400). Euler's totient φ(400) = 160 numbers up to 400 share no factor with it.
- 4
The digits of 400 add up to 4, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 27 steps to reach 1.
LaTeX source of the formulas on this page
\[ 400 = 2^{4} \times 5^{2} \]400 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 15 |
| Sum of divisors | 961 |
| Euler totient φ(n) | 160 |
| Square | 160000 |
| Cube | 64000000 |
| Square root | 20 |
| Digit sum / digital root | 4 / 4 |
| Collatz steps to 1 | 27 |
| Scientific notation | 4 × |
| Perfect power |
400 in other forms
| Form | Value |
|---|---|
| In words | four hundred |
| Roman numerals | CD |
| Binary (base 2) | 110010000 |
| Octal (base 8) | 620 |
| Hexadecimal (base 16) | 190 |
| Base 3 | 112211 |
| As time | 400 seconds = 6 min 40 s |
Is 400 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (400 ÷ 2 = 200) | 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 | Yes (400 ÷ 4 = 100) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (400 ÷ 5 = 80) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 4) | 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 | Yes (400 ÷ 8 = 50) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 4) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (400 ÷ 10 = 40) | 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 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 400 a prime number?
No. 400 = × , so it is divisible by 2.
What are the factors of 400?
1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400.
What is 400 in binary?
110010000 (hexadecimal 190, octal 620).
What is the square root of 400?
20, because 20 × 20 = 400.
What is 400 in Roman numerals?
CD.
Is 400 divisible by 3?
No. Its digits add up to 4, which is not a multiple of 3.
What is special about the number 400?
400 is a perfect square (20²); a Harshad number: divisible by its digit sum 4.