The number 13380
13380 is a composite number with 24 divisors. Its prime factorisation is × 3 × 5 × 223. Divisors (24): 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 223, 446, 669, 892 … 13380.
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How to work it out
- 1
What is special about 13380: a Harshad number: divisible by its digit sum 15.
- 2
13380 is composite. Its prime factorisation is
- 3
The divisors add up to 37632; without 13380 itself that is 24252, so 13380 is abundant (24252 is more than 13380). Euler's totient φ(13380) = 3552 numbers up to 13380 share no factor with it.
- 4
The digits of 13380 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 138 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13380 = 2^{2} \times 3 \times 5 \times 223 \]13380 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 37632 |
| Euler totient φ(n) | 3552 |
| Square | 179024400 |
| Cube | 2395346472000 |
| Square root | 115.671950 (= 2√3345) |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 138 |
| Scientific notation | 1.338 × |
13380 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand three hundred and eighty |
| Binary (base 2) | 11010001000100 |
| Octal (base 8) | 32104 |
| Hexadecimal (base 16) | 3444 |
| Base 3 | 200100120 |
| As time | 13380 seconds = 3 h 43 min 0 s |
Is 13380 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (13380 ÷ 2 = 6690) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (13380 ÷ 3 = 4460) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (13380 ÷ 4 = 3345) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (13380 ÷ 5 = 2676) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (13380 ÷ 6 = 2230) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 | No (remainder 4) | 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 (13380 ÷ 10 = 1338) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (13380 ÷ 12 = 1115) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 13380 a prime number?
No. 13380 = × 3 × 5 × 223, so it is divisible by 2.
What are the factors of 13380?
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 223, 446, 669, 892, 1115, 1338, 2230, 2676, 3345, 4460, 6690, 13380.
What is 13380 in binary?
11010001000100 (hexadecimal 3444, octal 32104).
What is the square root of 13380?
About 115.6719, exactly 2√3345.
Is 13380 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 13380?
13380 is a Harshad number: divisible by its digit sum 15.