The number 10440
10440 is a triangular number: 1 + 2 + … + 144 = 10440. Its prime factorisation is × × 5 × 29. Divisors (48): 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 29, 30 … 10440.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 10440: a triangular number: 1 + 2 + … + 144 = 10440; a Harshad number: divisible by its digit sum 9.
- 2
10440 is composite. Its prime factorisation is
- 3
The divisors add up to 35100; without 10440 itself that is 24660, so 10440 is abundant (24660 is more than 10440). Euler's totient φ(10440) = 2688 numbers up to 10440 share no factor with it.
- 4
The digits of 10440 add up to 9, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 55 steps to reach 1.
LaTeX source of the formulas on this page
\[ 10440 = 2^{3} \times 3^{2} \times 5 \times 29 \]10440 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 35100 |
| Euler totient φ(n) | 2688 |
| Square | 108993600 |
| Cube | 1137893184000 |
| Square root | 102.176318 (= 6√290) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 55 |
| Scientific notation | 1.044 × |
10440 in other forms
| Form | Value |
|---|---|
| In words | ten thousand four hundred and forty |
| Binary (base 2) | 10100011001000 |
| Octal (base 8) | 24310 |
| Hexadecimal (base 16) | 28C8 |
| Base 3 | 112022200 |
| As time | 10440 seconds = 2 h 54 min 0 s |
Is 10440 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (10440 ÷ 2 = 5220) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (10440 ÷ 3 = 3480) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (10440 ÷ 4 = 2610) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (10440 ÷ 5 = 2088) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (10440 ÷ 6 = 1740) | 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 (10440 ÷ 8 = 1305) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (10440 ÷ 9 = 1160) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (10440 ÷ 10 = 1044) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (10440 ÷ 12 = 870) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 10440 a prime number?
No. 10440 = × × 5 × 29, so it is divisible by 2.
What are the factors of 10440?
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 29, 30, 36, 40, 45, 58, 60, 72, 87, 90, 116, 120, 145, 174, 180, 232, 261, 290, 348, 360, 435, 522, 580, 696, 870, 1044, 1160, 1305, 1740, 2088, 2610, 3480, 5220, 10440.
What is 10440 in binary?
10100011001000 (hexadecimal 28C8, octal 24310).
What is the square root of 10440?
About 102.1763, exactly 6√290.
Is 10440 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 10440?
10440 is a triangular number: 1 + 2 + … + 144 = 10440; a Harshad number: divisible by its digit sum 9.