The number 13980
13980 is a composite number with 24 divisors. Its prime factorisation is × 3 × 5 × 233. Divisors (24): 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 233, 466, 699, 932 … 13980.
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How to work it out
- 1
13980 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
13980 is composite. Its prime factorisation is
- 3
The divisors add up to 39312; without 13980 itself that is 25332, so 13980 is abundant (25332 is more than 13980). Euler's totient φ(13980) = 3712 numbers up to 13980 share no factor with it.
- 4
The digits of 13980 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 58 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13980 = 2^{2} \times 3 \times 5 \times 233 \]13980 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 39312 |
| Euler totient φ(n) | 3712 |
| Square | 195440400 |
| Cube | 2732256792000 |
| Square root | 118.237050 (= 2√3495) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 58 |
| Scientific notation | 1.398 × |
13980 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand nine hundred and eighty |
| Binary (base 2) | 11011010011100 |
| Octal (base 8) | 33234 |
| Hexadecimal (base 16) | 369C |
| Base 3 | 201011210 |
| As time | 13980 seconds = 3 h 53 min 0 s |
Is 13980 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (13980 ÷ 2 = 6990) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (13980 ÷ 3 = 4660) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (13980 ÷ 4 = 3495) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (13980 ÷ 5 = 2796) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (13980 ÷ 6 = 2330) | 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 | No (remainder 3) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (13980 ÷ 10 = 1398) | 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 (13980 ÷ 12 = 1165) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 13980 a prime number?
No. 13980 = × 3 × 5 × 233, so it is divisible by 2.
What are the factors of 13980?
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 233, 466, 699, 932, 1165, 1398, 2330, 2796, 3495, 4660, 6990, 13980.
What is 13980 in binary?
11011010011100 (hexadecimal 369C, octal 33234).
What is the square root of 13980?
About 118.2371, exactly 2√3495.
Is 13980 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 13980?
It is a composite number with 24 divisors.