The number 5220
5220 is a composite number with 36 divisors. Its prime factorisation is × × 5 × 29. Divisors (36): 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 29, 30, 36, 45 … 5220.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 5220: a Harshad number: divisible by its digit sum 9.
- 2
5220 is composite. Its prime factorisation is
- 3
The divisors add up to 16380; without 5220 itself that is 11160, so 5220 is abundant (11160 is more than 5220). Euler's totient φ(5220) = 1344 numbers up to 5220 share no factor with it.
- 4
The digits of 5220 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
\[ 5220 = 2^{2} \times 3^{2} \times 5 \times 29 \]5220 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 16380 |
| Euler totient φ(n) | 1344 |
| Square | 27248400 |
| Cube | 142236648000 |
| Square root | 72.249567 (= 6√145) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 54 |
| Scientific notation | 5.22 × |
5220 in other forms
| Form | Value |
|---|---|
| In words | five thousand two hundred and twenty |
| Binary (base 2) | 1010001100100 |
| Octal (base 8) | 12144 |
| Hexadecimal (base 16) | 1464 |
| Base 3 | 21011100 |
| As time | 5220 seconds = 1 h 27 min 0 s |
Is 5220 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (5220 ÷ 2 = 2610) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (5220 ÷ 3 = 1740) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (5220 ÷ 4 = 1305) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (5220 ÷ 5 = 1044) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (5220 ÷ 6 = 870) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (5220 ÷ 9 = 580) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (5220 ÷ 10 = 522) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (5220 ÷ 12 = 435) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 5220 a prime number?
No. 5220 = × × 5 × 29, so it is divisible by 2.
What are the factors of 5220?
1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 29, 30, 36, 45, 58, 60, 87, 90, 116, 145, 174, 180, 261, 290, 348, 435, 522, 580, 870, 1044, 1305, 1740, 2610, 5220.
What is 5220 in binary?
1010001100100 (hexadecimal 1464, octal 12144).
What is the square root of 5220?
About 72.2496, exactly 6√145.
Is 5220 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 5220?
5220 is a Harshad number: divisible by its digit sum 9.