The number 40400
40400 is a composite number with 30 divisors. Its prime factorisation is × × 101. Divisors (30): 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 101, 200, 202 … 40400.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 40400: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 8.
- 2
40400 is composite. Its prime factorisation is
- 3
The divisors add up to 98022; without 40400 itself that is 57622, so 40400 is abundant (57622 is more than 40400). Euler's totient φ(40400) = 16000 numbers up to 40400 share no factor with it.
- 4
The digits of 40400 add up to 8, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 44 steps to reach 1.
LaTeX source of the formulas on this page
\[ 40400 = 2^{4} \times 5^{2} \times 101 \]40400 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 30 |
| Sum of divisors | 98022 |
| Euler totient φ(n) | 16000 |
| Square | 1632160000 |
| Cube | 65939264000000 |
| Square root | 200.997512 (= 20√101) |
| Digit sum / digital root | 8 / 8 |
| Collatz steps to 1 | 44 |
| Scientific notation | 4.04 × |
40400 in other forms
| Form | Value |
|---|---|
| In words | forty thousand four hundred |
| Binary (base 2) | 1001110111010000 |
| Octal (base 8) | 116720 |
| Hexadecimal (base 16) | 9DD0 |
| Base 3 | 2001102022 |
| As time | 40400 seconds = 11 h 13 min 20 s |
Is 40400 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (40400 ÷ 2 = 20200) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (40400 ÷ 4 = 10100) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (40400 ÷ 5 = 8080) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 2) | 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 (40400 ÷ 8 = 5050) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 8) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (40400 ÷ 10 = 4040) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 8) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 40400 a prime number?
No. 40400 = × × 101, so it is divisible by 2.
What are the factors of 40400?
1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 101, 200, 202, 400, 404, 505, 808, 1010, 1616, 2020, 2525, 4040, 5050, 8080, 10100, 20200, 40400.
What is 40400 in binary?
1001110111010000 (hexadecimal 9DD0, octal 116720).
What is the square root of 40400?
About 200.9975, exactly 20√101.
Is 40400 divisible by 3?
No. Its digits add up to 8, which is not a multiple of 3.
What is special about the number 40400?
40400 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 8.