The number 61440
61440 is a composite number with 52 divisors. Its prime factorisation is × 3 × 5. Divisors (52): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40 … 61440.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 61440: a Harshad number: divisible by its digit sum 15.
- 2
61440 is composite. Its prime factorisation is
- 3
The divisors add up to 196584; without 61440 itself that is 135144, so 61440 is abundant (135144 is more than 61440). Euler's totient φ(61440) = 16384 numbers up to 61440 share no factor with it.
- 4
The digits of 61440 add up to 15, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 29 steps to reach 1.
LaTeX source of the formulas on this page
\[ 61440 = 2^{12} \times 3 \times 5 \]61440 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 52 |
| Sum of divisors | 196584 |
| Euler totient φ(n) | 16384 |
| Square | 3774873600 |
| Cube | 231928233984000 |
| Square root | 247.870934 (= 64√15) |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 29 |
| Scientific notation | 6.144 × |
61440 in other forms
| Form | Value |
|---|---|
| In words | sixty-one thousand four hundred and forty |
| Binary (base 2) | 1111000000000000 |
| Octal (base 8) | 170000 |
| Hexadecimal (base 16) | F000 |
| Base 3 | 10010021120 |
| As time | 61440 seconds = 17 h 4 min 0 s |
Is 61440 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (61440 ÷ 2 = 30720) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (61440 ÷ 3 = 20480) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (61440 ÷ 4 = 15360) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (61440 ÷ 5 = 12288) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (61440 ÷ 6 = 10240) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 1) | 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 (61440 ÷ 8 = 7680) | 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 | Yes (61440 ÷ 10 = 6144) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 5) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (61440 ÷ 12 = 5120) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 61440 a prime number?
No. 61440 = × 3 × 5, so it is divisible by 2.
What are the factors of 61440?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 128, 160, 192, 240, 256, 320, 384, 480, 512, 640, 768, 960, 1024, 1280, 1536, 1920, 2048, 2560, 3072, 3840, 4096, 5120, 6144, 7680, 10240, 12288, 15360, 20480, 30720, 61440.
What is 61440 in binary?
1111000000000000 (hexadecimal F000, octal 170000).
What is the square root of 61440?
About 247.8709, exactly 64√15.
Is 61440 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 61440?
61440 is a Harshad number: divisible by its digit sum 15.