The number 72688
72688 is a composite number with 40 divisors. Its prime factorisation is × 7 × 11 × 59. Divisors (40): 1, 2, 4, 7, 8, 11, 14, 16, 22, 28, 44, 56, 59, 77, 88, 112 … 72688.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
72688 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
72688 is composite. Its prime factorisation is
- 3
The divisors add up to 178560; without 72688 itself that is 105872, so 72688 is abundant (105872 is more than 72688). Euler's totient φ(72688) = 27840 numbers up to 72688 share no factor with it.
- 4
The digits of 72688 add up to 31, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 187 steps to reach 1.
LaTeX source of the formulas on this page
\[ 72688 = 2^{4} \times 7 \times 11 \times 59 \]72688 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 40 |
| Sum of divisors | 178560 |
| Euler totient φ(n) | 27840 |
| Square | 5283545344 |
| Cube | 384050343964672 |
| Square root | 269.607122 (= 4√4543) |
| Digit sum / digital root | 31 / 4 |
| Collatz steps to 1 | 187 |
| Scientific notation | 7.2688 × |
72688 in other forms
| Form | Value |
|---|---|
| In words | seventy-two thousand six hundred and eighty-eight |
| Binary (base 2) | 10001101111110000 |
| Octal (base 8) | 215760 |
| Hexadecimal (base 16) | 11BF0 |
| Base 3 | 10200201011 |
| As time | 72688 seconds = 20 h 11 min 28 s |
Is 72688 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (72688 ÷ 2 = 36344) | 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 (72688 ÷ 4 = 18172) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 3) | 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 | Yes (72688 ÷ 7 = 10384) | 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 (72688 ÷ 8 = 9086) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 4) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 8) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (72688 ÷ 11 = 6608) | 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 72688 a prime number?
No. 72688 = × 7 × 11 × 59, so it is divisible by 2.
What are the factors of 72688?
1, 2, 4, 7, 8, 11, 14, 16, 22, 28, 44, 56, 59, 77, 88, 112, 118, 154, 176, 236, 308, 413, 472, 616, 649, 826, 944, 1232, 1298, 1652, 2596, 3304, 4543, 5192, 6608, 9086, 10384, 18172, 36344, 72688.
What is 72688 in binary?
10001101111110000 (hexadecimal 11BF0, octal 215760).
What is the square root of 72688?
About 269.6071, exactly 4√4543.
Is 72688 divisible by 3?
No. Its digits add up to 31, which is not a multiple of 3.
What is special about the number 72688?
It is a composite number with 40 divisors.