The number 31560
31560 is a composite number with 32 divisors. Its prime factorisation is × 3 × 5 × 263. Divisors (32): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120 … 31560.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 31560: a Harshad number: divisible by its digit sum 15.
- 2
31560 is composite. Its prime factorisation is
- 3
The divisors add up to 95040; without 31560 itself that is 63480, so 31560 is abundant (63480 is more than 31560). Euler's totient φ(31560) = 8384 numbers up to 31560 share no factor with it.
- 4
The digits of 31560 add up to 15, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 103 steps to reach 1.
LaTeX source of the formulas on this page
\[ 31560 = 2^{3} \times 3 \times 5 \times 263 \]31560 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 95040 |
| Euler totient φ(n) | 8384 |
| Square | 996033600 |
| Cube | 31434820416000 |
| Square root | 177.651344 (= 2√7890) |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 103 |
| Scientific notation | 3.156 × |
31560 in other forms
| Form | Value |
|---|---|
| In words | thirty-one thousand five hundred and sixty |
| Binary (base 2) | 111101101001000 |
| Octal (base 8) | 75510 |
| Hexadecimal (base 16) | 7B48 |
| Base 3 | 1121021220 |
| As time | 31560 seconds = 8 h 46 min 0 s |
Is 31560 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (31560 ÷ 2 = 15780) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (31560 ÷ 3 = 10520) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (31560 ÷ 4 = 7890) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (31560 ÷ 5 = 6312) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (31560 ÷ 6 = 5260) | 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 (31560 ÷ 8 = 3945) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (31560 ÷ 10 = 3156) | 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 (31560 ÷ 12 = 2630) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 31560 a prime number?
No. 31560 = × 3 × 5 × 263, so it is divisible by 2.
What are the factors of 31560?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120, 263, 526, 789, 1052, 1315, 1578, 2104, 2630, 3156, 3945, 5260, 6312, 7890, 10520, 15780, 31560.
What is 31560 in binary?
111101101001000 (hexadecimal 7B48, octal 75510).
What is the square root of 31560?
About 177.6513, exactly 2√7890.
Is 31560 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 31560?
31560 is a Harshad number: divisible by its digit sum 15.