The number 13920
13920 is a composite number with 48 divisors. Its prime factorisation is × 3 × 5 × 29. Divisors (48): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 29, 30, 32 … 13920.
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How to work it out
- 1
What is special about 13920: a Harshad number: divisible by its digit sum 15.
- 2
13920 is composite. Its prime factorisation is
- 3
The divisors add up to 45360; without 13920 itself that is 31440, so 13920 is abundant (31440 is more than 13920). Euler's totient φ(13920) = 3584 numbers up to 13920 share no factor with it.
- 4
The digits of 13920 add up to 15, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 32 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13920 = 2^{5} \times 3 \times 5 \times 29 \]13920 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 45360 |
| Euler totient φ(n) | 3584 |
| Square | 193766400 |
| Cube | 2697228288000 |
| Square root | 117.983050 (= 4√870) |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 32 |
| Scientific notation | 1.392 × |
13920 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand nine hundred and twenty |
| Binary (base 2) | 11011001100000 |
| Octal (base 8) | 33140 |
| Hexadecimal (base 16) | 3660 |
| Base 3 | 201002120 |
| As time | 13920 seconds = 3 h 52 min 0 s |
Is 13920 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (13920 ÷ 2 = 6960) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (13920 ÷ 3 = 4640) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (13920 ÷ 4 = 3480) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (13920 ÷ 5 = 2784) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (13920 ÷ 6 = 2320) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 (13920 ÷ 8 = 1740) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (13920 ÷ 10 = 1392) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 5) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (13920 ÷ 12 = 1160) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 13920 a prime number?
No. 13920 = × 3 × 5 × 29, so it is divisible by 2.
What are the factors of 13920?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 29, 30, 32, 40, 48, 58, 60, 80, 87, 96, 116, 120, 145, 160, 174, 232, 240, 290, 348, 435, 464, 480, 580, 696, 870, 928, 1160, 1392, 1740, 2320, 2784, 3480, 4640, 6960, 13920.
What is 13920 in binary?
11011001100000 (hexadecimal 3660, octal 33140).
What is the square root of 13920?
About 117.9830, exactly 4√870.
Is 13920 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 13920?
13920 is a Harshad number: divisible by its digit sum 15.