The number 40900
40900 is a composite number with 18 divisors. Its prime factorisation is × × 409. Divisors (18): 1, 2, 4, 5, 10, 20, 25, 50, 100, 409, 818, 1636, 2045, 4090, 8180, 10225 … 40900.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 40900: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
40900 is composite. Its prime factorisation is
- 3
The divisors add up to 88970; without 40900 itself that is 48070, so 40900 is abundant (48070 is more than 40900). Euler's totient φ(40900) = 16320 numbers up to 40900 share no factor with it.
- 4
The digits of 40900 add up to 13, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 62 steps to reach 1.
LaTeX source of the formulas on this page
\[ 40900 = 2^{2} \times 5^{2} \times 409 \]40900 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 18 |
| Sum of divisors | 88970 |
| Euler totient φ(n) | 16320 |
| Square | 1672810000 |
| Cube | 68417929000000 |
| Square root | 202.237484 (= 10√409) |
| Digit sum / digital root | 13 / 4 |
| Collatz steps to 1 | 62 |
| Scientific notation | 4.09 × |
40900 in other forms
| Form | Value |
|---|---|
| In words | forty thousand nine hundred |
| Binary (base 2) | 1001111111000100 |
| Octal (base 8) | 117704 |
| Hexadecimal (base 16) | 9FC4 |
| Base 3 | 2002002211 |
| As time | 40900 seconds = 11 h 21 min 40 s |
Is 40900 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (40900 ÷ 2 = 20450) | 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 (40900 ÷ 4 = 10225) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (40900 ÷ 5 = 8180) | 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 6) | 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 4) | 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 (40900 ÷ 10 = 4090) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 2) | 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 40900 a prime number?
No. 40900 = × × 409, so it is divisible by 2.
What are the factors of 40900?
1, 2, 4, 5, 10, 20, 25, 50, 100, 409, 818, 1636, 2045, 4090, 8180, 10225, 20450, 40900.
What is 40900 in binary?
1001111111000100 (hexadecimal 9FC4, octal 117704).
What is the square root of 40900?
About 202.2375, exactly 10√409.
Is 40900 divisible by 3?
No. Its digits add up to 13, which is not a multiple of 3.
What is special about the number 40900?
40900 is a happy number: repeatedly adding the squares of its digits reaches 1.