The number 13840
13840 is a composite number with 20 divisors. Its prime factorisation is × 5 × 173. Divisors (20): 1, 2, 4, 5, 8, 10, 16, 20, 40, 80, 173, 346, 692, 865, 1384, 1730 … 13840.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 13840: a Harshad number: divisible by its digit sum 16.
- 2
13840 is composite. Its prime factorisation is
- 3
The divisors add up to 32364; without 13840 itself that is 18524, so 13840 is abundant (18524 is more than 13840). Euler's totient φ(13840) = 5504 numbers up to 13840 share no factor with it.
- 4
The digits of 13840 add up to 16, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 151 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13840 = 2^{4} \times 5 \times 173 \]13840 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 20 |
| Sum of divisors | 32364 |
| Euler totient φ(n) | 5504 |
| Square | 191545600 |
| Cube | 2650991104000 |
| Square root | 117.643529 (= 4√865) |
| Digit sum / digital root | 16 / 7 |
| Collatz steps to 1 | 151 |
| Scientific notation | 1.384 × |
13840 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand eight hundred and forty |
| Binary (base 2) | 11011000010000 |
| Octal (base 8) | 33020 |
| Hexadecimal (base 16) | 3610 |
| Base 3 | 200222121 |
| As time | 13840 seconds = 3 h 50 min 40 s |
Is 13840 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (13840 ÷ 2 = 6920) | 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 (13840 ÷ 4 = 3460) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (13840 ÷ 5 = 2768) | 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 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 (13840 ÷ 8 = 1730) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 7) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (13840 ÷ 10 = 1384) | 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 13840 a prime number?
No. 13840 = × 5 × 173, so it is divisible by 2.
What are the factors of 13840?
1, 2, 4, 5, 8, 10, 16, 20, 40, 80, 173, 346, 692, 865, 1384, 1730, 2768, 3460, 6920, 13840.
What is 13840 in binary?
11011000010000 (hexadecimal 3610, octal 33020).
What is the square root of 13840?
About 117.6435, exactly 4√865.
Is 13840 divisible by 3?
No. Its digits add up to 16, which is not a multiple of 3.
What is special about the number 13840?
13840 is a Harshad number: divisible by its digit sum 16.