The number 40440
40440 is a composite number with 32 divisors. Its prime factorisation is × 3 × 5 × 337. Divisors (32): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120 … 40440.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 40440: a Harshad number: divisible by its digit sum 12.
- 2
40440 is composite. Its prime factorisation is
- 3
The divisors add up to 121680; without 40440 itself that is 81240, so 40440 is abundant (81240 is more than 40440). Euler's totient φ(40440) = 10752 numbers up to 40440 share no factor with it.
- 4
The digits of 40440 add up to 12, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 88 steps to reach 1.
LaTeX source of the formulas on this page
\[ 40440 = 2^{3} \times 3 \times 5 \times 337 \]40440 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 121680 |
| Euler totient φ(n) | 10752 |
| Square | 1635393600 |
| Cube | 66135317184000 |
| Square root | 201.096992 (= 2√10110) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 88 |
| Scientific notation | 4.044 × |
40440 in other forms
| Form | Value |
|---|---|
| In words | forty thousand four hundred and forty |
| Binary (base 2) | 1001110111111000 |
| Octal (base 8) | 116770 |
| Hexadecimal (base 16) | 9DF8 |
| Base 3 | 2001110210 |
| As time | 40440 seconds = 11 h 14 min 0 s |
Is 40440 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (40440 ÷ 2 = 20220) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (40440 ÷ 3 = 13480) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (40440 ÷ 4 = 10110) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (40440 ÷ 5 = 8088) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (40440 ÷ 6 = 6740) | 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 (40440 ÷ 8 = 5055) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (40440 ÷ 10 = 4044) | 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 | Yes (40440 ÷ 12 = 3370) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 40440 a prime number?
No. 40440 = × 3 × 5 × 337, so it is divisible by 2.
What are the factors of 40440?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120, 337, 674, 1011, 1348, 1685, 2022, 2696, 3370, 4044, 5055, 6740, 8088, 10110, 13480, 20220, 40440.
What is 40440 in binary?
1001110111111000 (hexadecimal 9DF8, octal 116770).
What is the square root of 40440?
About 201.0970, exactly 2√10110.
Is 40440 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 40440?
40440 is a Harshad number: divisible by its digit sum 12.