The number 31720
31720 is a composite number with 32 divisors. Its prime factorisation is × 5 × 13 × 61. Divisors (32): 1, 2, 4, 5, 8, 10, 13, 20, 26, 40, 52, 61, 65, 104, 122, 130 … 31720.
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How to work it out
- 1
What is special about 31720: a Harshad number: divisible by its digit sum 13.
- 2
31720 is composite. Its prime factorisation is
- 3
The divisors add up to 78120; without 31720 itself that is 46400, so 31720 is abundant (46400 is more than 31720). Euler's totient φ(31720) = 11520 numbers up to 31720 share no factor with it.
- 4
The digits of 31720 add up to 13, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 103 steps to reach 1.
LaTeX source of the formulas on this page
\[ 31720 = 2^{3} \times 5 \times 13 \times 61 \]31720 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 78120 |
| Euler totient φ(n) | 11520 |
| Square | 1006158400 |
| Cube | 31915344448000 |
| Square root | 178.101095 (= 2√7930) |
| Digit sum / digital root | 13 / 4 |
| Collatz steps to 1 | 103 |
| Scientific notation | 3.172 × |
31720 in other forms
| Form | Value |
|---|---|
| In words | thirty-one thousand seven hundred and twenty |
| Binary (base 2) | 111101111101000 |
| Octal (base 8) | 75750 |
| Hexadecimal (base 16) | 7BE8 |
| Base 3 | 1121111211 |
| As time | 31720 seconds = 8 h 48 min 40 s |
Is 31720 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (31720 ÷ 2 = 15860) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (31720 ÷ 4 = 7930) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (31720 ÷ 5 = 6344) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 4) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 (31720 ÷ 8 = 3965) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 4) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (31720 ÷ 10 = 3172) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 7) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 31720 a prime number?
No. 31720 = × 5 × 13 × 61, so it is divisible by 2.
What are the factors of 31720?
1, 2, 4, 5, 8, 10, 13, 20, 26, 40, 52, 61, 65, 104, 122, 130, 244, 260, 305, 488, 520, 610, 793, 1220, 1586, 2440, 3172, 3965, 6344, 7930, 15860, 31720.
What is 31720 in binary?
111101111101000 (hexadecimal 7BE8, octal 75750).
What is the square root of 31720?
About 178.1011, exactly 2√7930.
Is 31720 divisible by 3?
No. Its digits add up to 13, which is not a multiple of 3.
What is special about the number 31720?
31720 is a Harshad number: divisible by its digit sum 13.