The number 13872
13872 is a composite number with 30 divisors. Its prime factorisation is × 3 × . Divisors (30): 1, 2, 3, 4, 6, 8, 12, 16, 17, 24, 34, 48, 51, 68, 102, 136 … 13872.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
13872 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
13872 is composite. Its prime factorisation is
- 3
The divisors add up to 38068; without 13872 itself that is 24196, so 13872 is abundant (24196 is more than 13872). Euler's totient φ(13872) = 4352 numbers up to 13872 share no factor with it.
- 4
The digits of 13872 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 32 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13872 = 2^{4} \times 3 \times 17^{2} \]13872 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 30 |
| Sum of divisors | 38068 |
| Euler totient φ(n) | 4352 |
| Square | 192432384 |
| Cube | 2669422030848 |
| Square root | 117.779455 (= 68√3) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 32 |
| Scientific notation | 1.3872 × |
13872 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand eight hundred and seventy-two |
| Binary (base 2) | 11011000110000 |
| Octal (base 8) | 33060 |
| Hexadecimal (base 16) | 3630 |
| Base 3 | 201000210 |
| As time | 13872 seconds = 3 h 51 min 12 s |
Is 13872 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (13872 ÷ 2 = 6936) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (13872 ÷ 3 = 4624) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (13872 ÷ 4 = 3468) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 2) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (13872 ÷ 6 = 2312) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 (13872 ÷ 8 = 1734) | 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 | No (remainder 2) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (13872 ÷ 12 = 1156) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 13872 a prime number?
No. 13872 = × 3 × , so it is divisible by 2.
What are the factors of 13872?
1, 2, 3, 4, 6, 8, 12, 16, 17, 24, 34, 48, 51, 68, 102, 136, 204, 272, 289, 408, 578, 816, 867, 1156, 1734, 2312, 3468, 4624, 6936, 13872.
What is 13872 in binary?
11011000110000 (hexadecimal 3630, octal 33060).
What is the square root of 13872?
About 117.7795, exactly 68√3.
Is 13872 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 13872?
It is a composite number with 30 divisors.