The number 5280
5280 is a composite number with 48 divisors. Its prime factorisation is × 3 × 5 × 11. Divisors (48): 1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 16, 20, 22, 24, 30 … 5280.
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How to work it out
- 1
What is special about 5280: a Harshad number: divisible by its digit sum 15.
- 2
5280 is composite. Its prime factorisation is
- 3
The divisors add up to 18144; without 5280 itself that is 12864, so 5280 is abundant (12864 is more than 5280). Euler's totient φ(5280) = 1280 numbers up to 5280 share no factor with it.
- 4
The digits of 5280 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 116 steps to reach 1.
LaTeX source of the formulas on this page
\[ 5280 = 2^{5} \times 3 \times 5 \times 11 \]5280 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 18144 |
| Euler totient φ(n) | 1280 |
| Square | 27878400 |
| Cube | 147197952000 |
| Square root | 72.663608 (= 4√330) |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 116 |
| Scientific notation | 5.28 × |
5280 in other forms
| Form | Value |
|---|---|
| In words | five thousand two hundred and eighty |
| Binary (base 2) | 1010010100000 |
| Octal (base 8) | 12240 |
| Hexadecimal (base 16) | 14A0 |
| Base 3 | 21020120 |
| As time | 5280 seconds = 1 h 28 min 0 s |
Is 5280 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (5280 ÷ 2 = 2640) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (5280 ÷ 3 = 1760) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (5280 ÷ 4 = 1320) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (5280 ÷ 5 = 1056) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (5280 ÷ 6 = 880) | 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 (5280 ÷ 8 = 660) | 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 (5280 ÷ 10 = 528) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (5280 ÷ 11 = 480) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (5280 ÷ 12 = 440) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 5280 a prime number?
No. 5280 = × 3 × 5 × 11, so it is divisible by 2.
What are the factors of 5280?
1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 16, 20, 22, 24, 30, 32, 33, 40, 44, 48, 55, 60, 66, 80, 88, 96, 110, 120, 132, 160, 165, 176, 220, 240, 264, 330, 352, 440, 480, 528, 660, 880, 1056, 1320, 1760, 2640, 5280.
What is 5280 in binary?
1010010100000 (hexadecimal 14A0, octal 12240).
What is the square root of 5280?
About 72.6636, exactly 4√330.
Is 5280 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 5280?
5280 is a Harshad number: divisible by its digit sum 15.