The number 31320
31320 is a composite number with 64 divisors. Its prime factorisation is × × 5 × 29. Divisors (64): 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 27, 29 … 31320.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 31320: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 9.
- 2
31320 is composite. Its prime factorisation is
- 3
The divisors add up to 108000; without 31320 itself that is 76680, so 31320 is abundant (76680 is more than 31320). Euler's totient φ(31320) = 8064 numbers up to 31320 share no factor with it.
- 4
The digits of 31320 add up to 9, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 103 steps to reach 1.
LaTeX source of the formulas on this page
\[ 31320 = 2^{3} \times 3^{3} \times 5 \times 29 \]31320 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 64 |
| Sum of divisors | 108000 |
| Euler totient φ(n) | 8064 |
| Square | 980942400 |
| Cube | 30723115968000 |
| Square root | 176.974574 (= 6√870) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 103 |
| Scientific notation | 3.132 × |
31320 in other forms
| Form | Value |
|---|---|
| In words | thirty-one thousand three hundred and twenty |
| Binary (base 2) | 111101001011000 |
| Octal (base 8) | 75130 |
| Hexadecimal (base 16) | 7A58 |
| Base 3 | 1120222000 |
| As time | 31320 seconds = 8 h 42 min 0 s |
Is 31320 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (31320 ÷ 2 = 15660) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (31320 ÷ 3 = 10440) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (31320 ÷ 4 = 7830) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (31320 ÷ 5 = 6264) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (31320 ÷ 6 = 5220) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 (31320 ÷ 8 = 3915) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (31320 ÷ 9 = 3480) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (31320 ÷ 10 = 3132) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 3) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (31320 ÷ 12 = 2610) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 31320 a prime number?
No. 31320 = × × 5 × 29, so it is divisible by 2.
What are the factors of 31320?
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 27, 29, 30, 36, 40, 45, 54, 58, 60, 72, 87, 90, 108, 116, 120, 135, 145, 174, 180, 216, 232, 261, 270, 290, 348, 360, 435, 522, 540, 580, 696, 783, 870, 1044, 1080, 1160, 1305, 1566, 1740, 2088, 2610, 3132, 3480, 3915, 5220, 6264, 7830, 10440, 15660, 31320.
What is 31320 in binary?
111101001011000 (hexadecimal 7A58, octal 75130).
What is the square root of 31320?
About 176.9746, exactly 6√870.
Is 31320 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 31320?
31320 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 9.