The number 72800
72800 is a composite number with 72 divisors. Its prime factorisation is × × 7 × 13. Divisors (72): 1, 2, 4, 5, 7, 8, 10, 13, 14, 16, 20, 25, 26, 28, 32, 35 … 72800.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
72800 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
72800 is composite. Its prime factorisation is
- 3
The divisors add up to 218736; without 72800 itself that is 145936, so 72800 is abundant (145936 is more than 72800). Euler's totient φ(72800) = 23040 numbers up to 72800 share no factor with it.
- 4
The digits of 72800 add up to 17, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 24 steps to reach 1.
LaTeX source of the formulas on this page
\[ 72800 = 2^{5} \times 5^{2} \times 7 \times 13 \]72800 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 72 |
| Sum of divisors | 218736 |
| Euler totient φ(n) | 23040 |
| Square | 5299840000 |
| Cube | 385828352000000 |
| Square root | 269.814751 (= 20√182) |
| Digit sum / digital root | 17 / 8 |
| Collatz steps to 1 | 24 |
| Scientific notation | 7.28 × |
72800 in other forms
| Form | Value |
|---|---|
| In words | seventy-two thousand eight hundred |
| Binary (base 2) | 10001110001100000 |
| Octal (base 8) | 216140 |
| Hexadecimal (base 16) | 11C60 |
| Base 3 | 10200212022 |
| As time | 72800 seconds = 20 h 13 min 20 s |
Is 72800 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (72800 ÷ 2 = 36400) | 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 (72800 ÷ 4 = 18200) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (72800 ÷ 5 = 14560) | 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 | Yes (72800 ÷ 7 = 10400) | 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 (72800 ÷ 8 = 9100) | 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 (72800 ÷ 10 = 7280) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 2) | 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 72800 a prime number?
No. 72800 = × × 7 × 13, so it is divisible by 2.
What are the factors of 72800?
1, 2, 4, 5, 7, 8, 10, 13, 14, 16, 20, 25, 26, 28, 32, 35, 40, 50, 52, 56, 65, 70, 80, 91, 100, 104, 112, 130, 140, 160, 175, 182, 200, 208, 224, 260, 280, 325, 350, 364, 400, 416, 455, 520, 560, 650, 700, 728, 800, 910, 1040, 1120, 1300, 1400, 1456, 1820, 2080, 2275, 2600, 2800, 2912, 3640, 4550, 5200, 5600, 7280, 9100, 10400, 14560, 18200, 36400, 72800.
What is 72800 in binary?
10001110001100000 (hexadecimal 11C60, octal 216140).
What is the square root of 72800?
About 269.8148, exactly 20√182.
Is 72800 divisible by 3?
No. Its digits add up to 17, which is not a multiple of 3.
What is special about the number 72800?
It is a composite number with 72 divisors.