The number 40960
40960 is a composite number with 28 divisors. Its prime factorisation is × 5. Divisors (28): 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 128, 160, 256, 320 … 40960.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 40960: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
40960 is composite. Its prime factorisation is
- 3
The divisors add up to 98298; without 40960 itself that is 57338, so 40960 is abundant (57338 is more than 40960). Euler's totient φ(40960) = 16384 numbers up to 40960 share no factor with it.
- 4
The digits of 40960 add up to 19, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 18 steps to reach 1.
LaTeX source of the formulas on this page
\[ 40960 = 2^{13} \times 5 \]40960 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 28 |
| Sum of divisors | 98298 |
| Euler totient φ(n) | 16384 |
| Square | 1677721600 |
| Cube | 68719476736000 |
| Square root | 202.385770 (= 64√10) |
| Digit sum / digital root | 19 / 1 |
| Collatz steps to 1 | 18 |
| Scientific notation | 4.096 × |
40960 in other forms
| Form | Value |
|---|---|
| In words | forty thousand nine hundred and sixty |
| Binary (base 2) | 1010000000000000 |
| Octal (base 8) | 120000 |
| Hexadecimal (base 16) | A000 |
| Base 3 | 2002012001 |
| As time | 40960 seconds = 11 h 22 min 40 s |
Is 40960 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (40960 ÷ 2 = 20480) | 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 (40960 ÷ 4 = 10240) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (40960 ÷ 5 = 8192) | 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 | 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 (40960 ÷ 8 = 5120) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 1) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (40960 ÷ 10 = 4096) | 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 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 40960 a prime number?
No. 40960 = × 5, so it is divisible by 2.
What are the factors of 40960?
1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 128, 160, 256, 320, 512, 640, 1024, 1280, 2048, 2560, 4096, 5120, 8192, 10240, 20480, 40960.
What is 40960 in binary?
1010000000000000 (hexadecimal A000, octal 120000).
What is the square root of 40960?
About 202.3858, exactly 64√10.
Is 40960 divisible by 3?
No. Its digits add up to 19, which is not a multiple of 3.
What is special about the number 40960?
40960 is a happy number: repeatedly adding the squares of its digits reaches 1.