The number 5120
5120 is a composite number with 22 divisors. Its prime factorisation is × 5. Divisors (22): 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 128, 160, 256, 320 … 5120.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 5120: a Harshad number: divisible by its digit sum 8.
- 2
5120 is composite. Its prime factorisation is
- 3
The divisors add up to 12282; without 5120 itself that is 7162, so 5120 is abundant (7162 is more than 5120). Euler's totient φ(5120) = 2048 numbers up to 5120 share no factor with it.
- 4
The digits of 5120 add up to 8, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 15 steps to reach 1.
LaTeX source of the formulas on this page
\[ 5120 = 2^{10} \times 5 \]5120 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 22 |
| Sum of divisors | 12282 |
| Euler totient φ(n) | 2048 |
| Square | 26214400 |
| Cube | 134217728000 |
| Square root | 71.554175 (= 32√5) |
| Digit sum / digital root | 8 / 8 |
| Collatz steps to 1 | 15 |
| Scientific notation | 5.12 × |
5120 in other forms
| Form | Value |
|---|---|
| In words | five thousand one hundred and twenty |
| Binary (base 2) | 1010000000000 |
| Octal (base 8) | 12000 |
| Hexadecimal (base 16) | 1400 |
| Base 3 | 21000122 |
| As time | 5120 seconds = 1 h 25 min 20 s |
Is 5120 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (5120 ÷ 2 = 2560) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (5120 ÷ 4 = 1280) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (5120 ÷ 5 = 1024) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 2) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 (5120 ÷ 8 = 640) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 8) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (5120 ÷ 10 = 512) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 5) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 5120 a prime number?
No. 5120 = × 5, so it is divisible by 2.
What are the factors of 5120?
1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 128, 160, 256, 320, 512, 640, 1024, 1280, 2560, 5120.
What is 5120 in binary?
1010000000000 (hexadecimal 1400, octal 12000).
What is the square root of 5120?
About 71.5542, exactly 32√5.
Is 5120 divisible by 3?
No. Its digits add up to 8, which is not a multiple of 3.
What is special about the number 5120?
5120 is a Harshad number: divisible by its digit sum 8.