The number 13440
13440 is a composite number with 64 divisors. Its prime factorisation is × 3 × 5 × 7. Divisors (64): 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24 … 13440.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 13440: a Harshad number: divisible by its digit sum 12.
- 2
13440 is composite. Its prime factorisation is
- 3
The divisors add up to 48960; without 13440 itself that is 35520, so 13440 is abundant (35520 is more than 13440). Euler's totient φ(13440) = 3072 numbers up to 13440 share no factor with it.
- 4
The digits of 13440 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 45 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13440 = 2^{7} \times 3 \times 5 \times 7 \]13440 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 64 |
| Sum of divisors | 48960 |
| Euler totient φ(n) | 3072 |
| Square | 180633600 |
| Cube | 2427715584000 |
| Square root | 115.931014 (= 8√210) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 45 |
| Scientific notation | 1.344 × |
13440 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand four hundred and forty |
| Binary (base 2) | 11010010000000 |
| Octal (base 8) | 32200 |
| Hexadecimal (base 16) | 3480 |
| Base 3 | 200102210 |
| As time | 13440 seconds = 3 h 44 min 0 s |
Is 13440 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (13440 ÷ 2 = 6720) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (13440 ÷ 3 = 4480) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (13440 ÷ 4 = 3360) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (13440 ÷ 5 = 2688) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (13440 ÷ 6 = 2240) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (13440 ÷ 7 = 1920) | 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 (13440 ÷ 8 = 1680) | 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 (13440 ÷ 10 = 1344) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 9) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (13440 ÷ 12 = 1120) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 13440 a prime number?
No. 13440 = × 3 × 5 × 7, so it is divisible by 2.
What are the factors of 13440?
1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 28, 30, 32, 35, 40, 42, 48, 56, 60, 64, 70, 80, 84, 96, 105, 112, 120, 128, 140, 160, 168, 192, 210, 224, 240, 280, 320, 336, 384, 420, 448, 480, 560, 640, 672, 840, 896, 960, 1120, 1344, 1680, 1920, 2240, 2688, 3360, 4480, 6720, 13440.
What is 13440 in binary?
11010010000000 (hexadecimal 3480, octal 32200).
What is the square root of 13440?
About 115.9310, exactly 8√210.
Is 13440 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 13440?
13440 is a Harshad number: divisible by its digit sum 12.