The number 61728
61728 is a composite number with 24 divisors. Its prime factorisation is × 3 × 643. Divisors (24): 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 643, 1286, 1929, 2572 … 61728.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 61728: a Harshad number: divisible by its digit sum 24.
- 2
61728 is composite. Its prime factorisation is
- 3
The divisors add up to 162288; without 61728 itself that is 100560, so 61728 is abundant (100560 is more than 61728). Euler's totient φ(61728) = 20544 numbers up to 61728 share no factor with it.
- 4
The digits of 61728 add up to 24, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 60 steps to reach 1.
LaTeX source of the formulas on this page
\[ 61728 = 2^{5} \times 3 \times 643 \]61728 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 162288 |
| Euler totient φ(n) | 20544 |
| Square | 3810345984 |
| Cube | 235205036900352 |
| Square root | 248.451202 (= 4√3858) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 60 |
| Scientific notation | 6.1728 × |
61728 in other forms
| Form | Value |
|---|---|
| In words | sixty-one thousand seven hundred and twenty-eight |
| Binary (base 2) | 1111000100100000 |
| Octal (base 8) | 170440 |
| Hexadecimal (base 16) | F120 |
| Base 3 | 10010200020 |
| As time | 61728 seconds = 17 h 8 min 48 s |
Is 61728 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (61728 ÷ 2 = 30864) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (61728 ÷ 3 = 20576) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (61728 ÷ 4 = 15432) | 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 | Yes (61728 ÷ 6 = 10288) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 (61728 ÷ 8 = 7716) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | 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 7) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (61728 ÷ 12 = 5144) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 61728 a prime number?
No. 61728 = × 3 × 643, so it is divisible by 2.
What are the factors of 61728?
1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 643, 1286, 1929, 2572, 3858, 5144, 7716, 10288, 15432, 20576, 30864, 61728.
What is 61728 in binary?
1111000100100000 (hexadecimal F120, octal 170440).
What is the square root of 61728?
About 248.4512, exactly 4√3858.
Is 61728 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 61728?
61728 is a Harshad number: divisible by its digit sum 24.