The number 13140
13140 is a composite number with 36 divisors. Its prime factorisation is × × 5 × 73. Divisors (36): 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60 … 13140.
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How to work it out
- 1
What is special about 13140: a Harshad number: divisible by its digit sum 9.
- 2
13140 is composite. Its prime factorisation is
- 3
The divisors add up to 40404; without 13140 itself that is 27264, so 13140 is abundant (27264 is more than 13140). Euler's totient φ(13140) = 3456 numbers up to 13140 share no factor with it.
- 4
The digits of 13140 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 32 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13140 = 2^{2} \times 3^{2} \times 5 \times 73 \]13140 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 40404 |
| Euler totient φ(n) | 3456 |
| Square | 172659600 |
| Cube | 2268747144000 |
| Square root | 114.629839 (= 6√365) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 32 |
| Scientific notation | 1.314 × |
13140 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand one hundred and forty |
| Binary (base 2) | 11001101010100 |
| Octal (base 8) | 31524 |
| Hexadecimal (base 16) | 3354 |
| Base 3 | 200000200 |
| As time | 13140 seconds = 3 h 39 min 0 s |
Is 13140 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (13140 ÷ 2 = 6570) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (13140 ÷ 3 = 4380) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (13140 ÷ 4 = 3285) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (13140 ÷ 5 = 2628) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (13140 ÷ 6 = 2190) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 1) | 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 | Yes (13140 ÷ 9 = 1460) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (13140 ÷ 10 = 1314) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (13140 ÷ 12 = 1095) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 13140 a prime number?
No. 13140 = × × 5 × 73, so it is divisible by 2.
What are the factors of 13140?
1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 73, 90, 146, 180, 219, 292, 365, 438, 657, 730, 876, 1095, 1314, 1460, 2190, 2628, 3285, 4380, 6570, 13140.
What is 13140 in binary?
11001101010100 (hexadecimal 3354, octal 31524).
What is the square root of 13140?
About 114.6298, exactly 6√365.
Is 13140 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 13140?
13140 is a Harshad number: divisible by its digit sum 9.