The number 31800
31800 is a composite number with 48 divisors. Its prime factorisation is × 3 × × 53. Divisors (48): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50 … 31800.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 31800: a Harshad number: divisible by its digit sum 12.
- 2
31800 is composite. Its prime factorisation is
- 3
The divisors add up to 100440; without 31800 itself that is 68640, so 31800 is abundant (68640 is more than 31800). Euler's totient φ(31800) = 8320 numbers up to 31800 share no factor with it.
- 4
The digits of 31800 add up to 12, 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
\[ 31800 = 2^{3} \times 3 \times 5^{2} \times 53 \]31800 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 100440 |
| Euler totient φ(n) | 8320 |
| Square | 1011240000 |
| Cube | 32157432000000 |
| Square root | 178.325545 (= 10√318) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 54 |
| Scientific notation | 3.18 × |
31800 in other forms
| Form | Value |
|---|---|
| In words | thirty-one thousand eight hundred |
| Binary (base 2) | 111110000111000 |
| Octal (base 8) | 76070 |
| Hexadecimal (base 16) | 7C38 |
| Base 3 | 1121121210 |
| As time | 31800 seconds = 8 h 50 min 0 s |
Is 31800 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (31800 ÷ 2 = 15900) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (31800 ÷ 3 = 10600) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (31800 ÷ 4 = 7950) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (31800 ÷ 5 = 6360) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (31800 ÷ 6 = 5300) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | 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 (31800 ÷ 8 = 3975) | 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 (31800 ÷ 10 = 3180) | 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 (31800 ÷ 12 = 2650) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 31800 a prime number?
No. 31800 = × 3 × × 53, so it is divisible by 2.
What are the factors of 31800?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 53, 60, 75, 100, 106, 120, 150, 159, 200, 212, 265, 300, 318, 424, 530, 600, 636, 795, 1060, 1272, 1325, 1590, 2120, 2650, 3180, 3975, 5300, 6360, 7950, 10600, 15900, 31800.
What is 31800 in binary?
111110000111000 (hexadecimal 7C38, octal 76070).
What is the square root of 31800?
About 178.3255, exactly 10√318.
Is 31800 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 31800?
31800 is a Harshad number: divisible by its digit sum 12.