The number 4040
4040 is a composite number with 16 divisors. Its prime factorisation is × 5 × 101. Divisors (16): 1, 2, 4, 5, 8, 10, 20, 40, 101, 202, 404, 505, 808, 1010, 2020, 4040.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 4040: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 8.
- 2
4040 is composite. Its prime factorisation is
- 3
The divisors add up to 9180; without 4040 itself that is 5140, so 4040 is abundant (5140 is more than 4040). Euler's totient φ(4040) = 1600 numbers up to 4040 share no factor with it.
- 4
The digits of 4040 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 64 steps to reach 1.
LaTeX source of the formulas on this page
\[ 4040 = 2^{3} \times 5 \times 101 \]4040 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 9180 |
| Euler totient φ(n) | 1600 |
| Square | 16321600 |
| Cube | 65939264000 |
| Square root | 63.560994 (= 2√1010) |
| Digit sum / digital root | 8 / 8 |
| Collatz steps to 1 | 64 |
| Scientific notation | 4.04 × |
4040 in other forms
| Form | Value |
|---|---|
| In words | four thousand and forty |
| Binary (base 2) | 111111001000 |
| Octal (base 8) | 7710 |
| Hexadecimal (base 16) | FC8 |
| Base 3 | 12112122 |
| As time | 4040 seconds = 1 h 7 min 20 s |
Is 4040 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (4040 ÷ 2 = 2020) | 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 (4040 ÷ 4 = 1010) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (4040 ÷ 5 = 808) | 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 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 (4040 ÷ 8 = 505) | 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 (4040 ÷ 10 = 404) | 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 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 4040 a prime number?
No. 4040 = × 5 × 101, so it is divisible by 2.
What are the factors of 4040?
1, 2, 4, 5, 8, 10, 20, 40, 101, 202, 404, 505, 808, 1010, 2020, 4040.
What is 4040 in binary?
111111001000 (hexadecimal FC8, octal 7710).
What is the square root of 4040?
About 63.5610, exactly 2√1010.
Is 4040 divisible by 3?
No. Its digits add up to 8, which is not a multiple of 3.
What is special about the number 4040?
4040 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 8.