The number 31224
31224 is a composite number with 16 divisors. Its prime factorisation is × 3 × 1301. Divisors (16): 1, 2, 3, 4, 6, 8, 12, 24, 1301, 2602, 3903, 5204, 7806, 10408, 15612, 31224.
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How to work it out
- 1
What is special about 31224: a Harshad number: divisible by its digit sum 12.
- 2
31224 is composite. Its prime factorisation is
- 3
The divisors add up to 78120; without 31224 itself that is 46896, so 31224 is abundant (46896 is more than 31224). Euler's totient φ(31224) = 10400 numbers up to 31224 share no factor with it.
- 4
The digits of 31224 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 178 steps to reach 1.
LaTeX source of the formulas on this page
\[ 31224 = 2^{3} \times 3 \times 1301 \]31224 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 78120 |
| Euler totient φ(n) | 10400 |
| Square | 974938176 |
| Cube | 30441469607424 |
| Square root | 176.703141 (= 2√7806) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 178 |
| Scientific notation | 3.1224 × |
31224 in other forms
| Form | Value |
|---|---|
| In words | thirty-one thousand two hundred and twenty-four |
| Binary (base 2) | 111100111111000 |
| Octal (base 8) | 74770 |
| Hexadecimal (base 16) | 79F8 |
| Base 3 | 1120211110 |
| As time | 31224 seconds = 8 h 40 min 24 s |
Is 31224 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (31224 ÷ 2 = 15612) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (31224 ÷ 3 = 10408) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (31224 ÷ 4 = 7806) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 4) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (31224 ÷ 6 = 5204) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 (31224 ÷ 8 = 3903) | 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 4) | 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 (31224 ÷ 12 = 2602) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 31224 a prime number?
No. 31224 = × 3 × 1301, so it is divisible by 2.
What are the factors of 31224?
1, 2, 3, 4, 6, 8, 12, 24, 1301, 2602, 3903, 5204, 7806, 10408, 15612, 31224.
What is 31224 in binary?
111100111111000 (hexadecimal 79F8, octal 74770).
What is the square root of 31224?
About 176.7031, exactly 2√7806.
Is 31224 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 31224?
31224 is a Harshad number: divisible by its digit sum 12.