The number 13320
13320 is a composite number with 48 divisors. Its prime factorisation is × × 5 × 37. Divisors (48): 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36 … 13320.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 13320: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 9.
- 2
13320 is composite. Its prime factorisation is
- 3
The divisors add up to 44460; without 13320 itself that is 31140, so 13320 is abundant (31140 is more than 13320). Euler's totient φ(13320) = 3456 numbers up to 13320 share no factor with it.
- 4
The digits of 13320 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 182 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13320 = 2^{3} \times 3^{2} \times 5 \times 37 \]13320 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 44460 |
| Euler totient φ(n) | 3456 |
| Square | 177422400 |
| Cube | 2363266368000 |
| Square root | 115.412304 (= 6√370) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 182 |
| Scientific notation | 1.332 × |
13320 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand three hundred and twenty |
| Binary (base 2) | 11010000001000 |
| Octal (base 8) | 32010 |
| Hexadecimal (base 16) | 3408 |
| Base 3 | 200021100 |
| As time | 13320 seconds = 3 h 42 min 0 s |
Is 13320 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (13320 ÷ 2 = 6660) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (13320 ÷ 3 = 4440) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (13320 ÷ 4 = 3330) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (13320 ÷ 5 = 2664) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (13320 ÷ 6 = 2220) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | 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 (13320 ÷ 8 = 1665) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (13320 ÷ 9 = 1480) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (13320 ÷ 10 = 1332) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 10) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (13320 ÷ 12 = 1110) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 13320 a prime number?
No. 13320 = × × 5 × 37, so it is divisible by 2.
What are the factors of 13320?
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 37, 40, 45, 60, 72, 74, 90, 111, 120, 148, 180, 185, 222, 296, 333, 360, 370, 444, 555, 666, 740, 888, 1110, 1332, 1480, 1665, 2220, 2664, 3330, 4440, 6660, 13320.
What is 13320 in binary?
11010000001000 (hexadecimal 3408, octal 32010).
What is the square root of 13320?
About 115.4123, exactly 6√370.
Is 13320 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 13320?
13320 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 9.