The number 13944
13944 is a composite number with 32 divisors. Its prime factorisation is × 3 × 7 × 83. Divisors (32): 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 83, 84 … 13944.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 13944: a Harshad number: divisible by its digit sum 21.
- 2
13944 is composite. Its prime factorisation is
- 3
The divisors add up to 40320; without 13944 itself that is 26376, so 13944 is abundant (26376 is more than 13944). Euler's totient φ(13944) = 3936 numbers up to 13944 share no factor with it.
- 4
The digits of 13944 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 182 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13944 = 2^{3} \times 3 \times 7 \times 83 \]13944 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 40320 |
| Euler totient φ(n) | 3936 |
| Square | 194435136 |
| Cube | 2711203536384 |
| Square root | 118.084715 (= 2√3486) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 182 |
| Scientific notation | 1.3944 × |
13944 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand nine hundred and forty-four |
| Binary (base 2) | 11011001111000 |
| Octal (base 8) | 33170 |
| Hexadecimal (base 16) | 3678 |
| Base 3 | 201010110 |
| As time | 13944 seconds = 3 h 52 min 24 s |
Is 13944 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (13944 ÷ 2 = 6972) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (13944 ÷ 3 = 4648) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (13944 ÷ 4 = 3486) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 4) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (13944 ÷ 6 = 2324) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (13944 ÷ 7 = 1992) | 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 (13944 ÷ 8 = 1743) | 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 | No (remainder 4) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 7) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (13944 ÷ 12 = 1162) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 13944 a prime number?
No. 13944 = × 3 × 7 × 83, so it is divisible by 2.
What are the factors of 13944?
1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 83, 84, 166, 168, 249, 332, 498, 581, 664, 996, 1162, 1743, 1992, 2324, 3486, 4648, 6972, 13944.
What is 13944 in binary?
11011001111000 (hexadecimal 3678, octal 33170).
What is the square root of 13944?
About 118.0847, exactly 2√3486.
Is 13944 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 13944?
13944 is a Harshad number: divisible by its digit sum 21.