The number 5200
5200 is a composite number with 30 divisors. Its prime factorisation is × × 13. Divisors (30): 1, 2, 4, 5, 8, 10, 13, 16, 20, 25, 26, 40, 50, 52, 65, 80 … 5200.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
5200 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
5200 is composite. Its prime factorisation is
- 3
The divisors add up to 13454; without 5200 itself that is 8254, so 5200 is abundant (8254 is more than 5200). Euler's totient φ(5200) = 1920 numbers up to 5200 share no factor with it.
- 4
The digits of 5200 add up to 7, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 28 steps to reach 1.
LaTeX source of the formulas on this page
\[ 5200 = 2^{4} \times 5^{2} \times 13 \]5200 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 30 |
| Sum of divisors | 13454 |
| Euler totient φ(n) | 1920 |
| Square | 27040000 |
| Cube | 140608000000 |
| Square root | 72.111026 (= 20√13) |
| Digit sum / digital root | 7 / 7 |
| Collatz steps to 1 | 28 |
| Scientific notation | 5.2 × |
5200 in other forms
| Form | Value |
|---|---|
| In words | five thousand two hundred |
| Binary (base 2) | 1010001010000 |
| Octal (base 8) | 12120 |
| Hexadecimal (base 16) | 1450 |
| Base 3 | 21010121 |
| As time | 5200 seconds = 1 h 26 min 40 s |
Is 5200 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (5200 ÷ 2 = 2600) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (5200 ÷ 4 = 1300) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (5200 ÷ 5 = 1040) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 4) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | 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 (5200 ÷ 8 = 650) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 7) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (5200 ÷ 10 = 520) | 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 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 5200 a prime number?
No. 5200 = × × 13, so it is divisible by 2.
What are the factors of 5200?
1, 2, 4, 5, 8, 10, 13, 16, 20, 25, 26, 40, 50, 52, 65, 80, 100, 104, 130, 200, 208, 260, 325, 400, 520, 650, 1040, 1300, 2600, 5200.
What is 5200 in binary?
1010001010000 (hexadecimal 1450, octal 12120).
What is the square root of 5200?
About 72.1110, exactly 20√13.
Is 5200 divisible by 3?
No. Its digits add up to 7, which is not a multiple of 3.
What is special about the number 5200?
It is a composite number with 30 divisors.