The number 5310
5310 is a composite number with 24 divisors. Its prime factorisation is 2 × × 5 × 59. Divisors (24): 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 59, 90, 118, 177, 295 … 5310.
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How to work it out
- 1
What is special about 5310: a Harshad number: divisible by its digit sum 9.
- 2
5310 is composite. Its prime factorisation is
- 3
The divisors add up to 14040; without 5310 itself that is 8730, so 5310 is abundant (8730 is more than 5310). Euler's totient φ(5310) = 1392 numbers up to 5310 share no factor with it.
- 4
The digits of 5310 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 54 steps to reach 1.
LaTeX source of the formulas on this page
\[ 5310 = 2 \times 3^{2} \times 5 \times 59 \]5310 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 14040 |
| Euler totient φ(n) | 1392 |
| Square | 28196100 |
| Cube | 149721291000 |
| Square root | 72.869747 (= 3√590) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 54 |
| Scientific notation | 5.31 × |
5310 in other forms
| Form | Value |
|---|---|
| In words | five thousand three hundred and ten |
| Binary (base 2) | 1010010111110 |
| Octal (base 8) | 12276 |
| Hexadecimal (base 16) | 14BE |
| Base 3 | 21021200 |
| As time | 5310 seconds = 1 h 28 min 30 s |
Is 5310 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (5310 ÷ 2 = 2655) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (5310 ÷ 3 = 1770) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 2) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (5310 ÷ 5 = 1062) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (5310 ÷ 6 = 885) | 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 | No (remainder 6) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (5310 ÷ 9 = 590) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (5310 ÷ 10 = 531) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 8) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 6) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 5310 a prime number?
No. 5310 = 2 × × 5 × 59, so it is divisible by 2.
What are the factors of 5310?
1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 59, 90, 118, 177, 295, 354, 531, 590, 885, 1062, 1770, 2655, 5310.
What is 5310 in binary?
1010010111110 (hexadecimal 14BE, octal 12276).
What is the square root of 5310?
About 72.8697, exactly 3√590.
Is 5310 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 5310?
5310 is a Harshad number: divisible by its digit sum 9.