The number 31872
31872 is a composite number with 32 divisors. Its prime factorisation is × 3 × 83. Divisors (32): 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 83, 96, 128, 166 … 31872.
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How to work it out
- 1
31872 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
31872 is composite. Its prime factorisation is
- 3
The divisors add up to 85680; without 31872 itself that is 53808, so 31872 is abundant (53808 is more than 31872). Euler's totient φ(31872) = 10496 numbers up to 31872 share no factor with it.
- 4
The digits of 31872 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 54 steps to reach 1.
LaTeX source of the formulas on this page
\[ 31872 = 2^{7} \times 3 \times 83 \]31872 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 85680 |
| Euler totient φ(n) | 10496 |
| Square | 1015824384 |
| Cube | 32376354766848 |
| Square root | 178.527309 (= 8√498) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 54 |
| Scientific notation | 3.1872 × |
31872 in other forms
| Form | Value |
|---|---|
| In words | thirty-one thousand eight hundred and seventy-two |
| Binary (base 2) | 111110010000000 |
| Octal (base 8) | 76200 |
| Hexadecimal (base 16) | 7C80 |
| Base 3 | 1121201110 |
| As time | 31872 seconds = 8 h 51 min 12 s |
Is 31872 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (31872 ÷ 2 = 15936) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (31872 ÷ 3 = 10624) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (31872 ÷ 4 = 7968) | 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 (31872 ÷ 6 = 5312) | 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 | Yes (31872 ÷ 8 = 3984) | 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 5) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (31872 ÷ 12 = 2656) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 31872 a prime number?
No. 31872 = × 3 × 83, so it is divisible by 2.
What are the factors of 31872?
1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 83, 96, 128, 166, 192, 249, 332, 384, 498, 664, 996, 1328, 1992, 2656, 3984, 5312, 7968, 10624, 15936, 31872.
What is 31872 in binary?
111110010000000 (hexadecimal 7C80, octal 76200).
What is the square root of 31872?
About 178.5273, exactly 8√498.
Is 31872 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 31872?
It is a composite number with 32 divisors.