The number 61344
61344 is a composite number with 48 divisors. Its prime factorisation is × × 71. Divisors (48): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54 … 61344.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 61344: a Harshad number: divisible by its digit sum 18.
- 2
61344 is composite. Its prime factorisation is
- 3
The divisors add up to 181440; without 61344 itself that is 120096, so 61344 is abundant (120096 is more than 61344). Euler's totient φ(61344) = 20160 numbers up to 61344 share no factor with it.
- 4
The digits of 61344 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 60 steps to reach 1.
LaTeX source of the formulas on this page
\[ 61344 = 2^{5} \times 3^{3} \times 71 \]61344 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 181440 |
| Euler totient φ(n) | 20160 |
| Square | 3763086336 |
| Cube | 230842768195584 |
| Square root | 247.677209 (= 12√426) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 60 |
| Scientific notation | 6.1344 × |
61344 in other forms
| Form | Value |
|---|---|
| In words | sixty-one thousand three hundred and forty-four |
| Binary (base 2) | 1110111110100000 |
| Octal (base 8) | 167640 |
| Hexadecimal (base 16) | EFA0 |
| Base 3 | 10010011000 |
| As time | 61344 seconds = 17 h 2 min 24 s |
Is 61344 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (61344 ÷ 2 = 30672) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (61344 ÷ 3 = 20448) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (61344 ÷ 4 = 15336) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 4) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (61344 ÷ 6 = 10224) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 (61344 ÷ 8 = 7668) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (61344 ÷ 9 = 6816) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 4) | 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 | Yes (61344 ÷ 12 = 5112) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 61344 a prime number?
No. 61344 = × × 71, so it is divisible by 2.
What are the factors of 61344?
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 71, 72, 96, 108, 142, 144, 213, 216, 284, 288, 426, 432, 568, 639, 852, 864, 1136, 1278, 1704, 1917, 2272, 2556, 3408, 3834, 5112, 6816, 7668, 10224, 15336, 20448, 30672, 61344.
What is 61344 in binary?
1110111110100000 (hexadecimal EFA0, octal 167640).
What is the square root of 61344?
About 247.6772, exactly 12√426.
Is 61344 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 61344?
61344 is a Harshad number: divisible by its digit sum 18.