The number 72128
72128 is a composite number with 42 divisors. Its prime factorisation is × × 23. Divisors (42): 1, 2, 4, 7, 8, 14, 16, 23, 28, 32, 46, 49, 56, 64, 92, 98 … 72128.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
72128 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
72128 is composite. Its prime factorisation is
- 3
The divisors add up to 173736; without 72128 itself that is 101608, so 72128 is abundant (101608 is more than 72128). Euler's totient φ(72128) = 29568 numbers up to 72128 share no factor with it.
- 4
The digits of 72128 add up to 20, and repeating that until one digit is left gives the digital root 2. The Collatz sequence (halve if even, else 3n+1) takes 143 steps to reach 1.
LaTeX source of the formulas on this page
\[ 72128 = 2^{6} \times 7^{2} \times 23 \]72128 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 42 |
| Sum of divisors | 173736 |
| Euler totient φ(n) | 29568 |
| Square | 5202448384 |
| Cube | 375242197041152 |
| Square root | 268.566565 (= 56√23) |
| Digit sum / digital root | 20 / 2 |
| Collatz steps to 1 | 143 |
| Scientific notation | 7.2128 × |
72128 in other forms
| Form | Value |
|---|---|
| In words | seventy-two thousand one hundred and twenty-eight |
| Binary (base 2) | 10001100111000000 |
| Octal (base 8) | 214700 |
| Hexadecimal (base 16) | 119C0 |
| Base 3 | 10122221102 |
| As time | 72128 seconds = 20 h 2 min 8 s |
Is 72128 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (72128 ÷ 2 = 36064) | 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 (72128 ÷ 4 = 18032) | 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 2) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (72128 ÷ 7 = 10304) | 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 (72128 ÷ 8 = 9016) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 2) | 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 | No (remainder 1) | 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 72128 a prime number?
No. 72128 = × × 23, so it is divisible by 2.
What are the factors of 72128?
1, 2, 4, 7, 8, 14, 16, 23, 28, 32, 46, 49, 56, 64, 92, 98, 112, 161, 184, 196, 224, 322, 368, 392, 448, 644, 736, 784, 1127, 1288, 1472, 1568, 2254, 2576, 3136, 4508, 5152, 9016, 10304, 18032, 36064, 72128.
What is 72128 in binary?
10001100111000000 (hexadecimal 119C0, octal 214700).
What is the square root of 72128?
About 268.5666, exactly 56√23.
Is 72128 divisible by 3?
No. Its digits add up to 20, which is not a multiple of 3.
What is special about the number 72128?
It is a composite number with 42 divisors.