The number 46400
46400 is a composite number with 42 divisors. Its prime factorisation is × × 29. Divisors (42): 1, 2, 4, 5, 8, 10, 16, 20, 25, 29, 32, 40, 50, 58, 64, 80 … 46400.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 46400: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
46400 is composite. Its prime factorisation is
- 3
The divisors add up to 118110; without 46400 itself that is 71710, so 46400 is abundant (71710 is more than 46400). Euler's totient φ(46400) = 17920 numbers up to 46400 share no factor with it.
- 4
The digits of 46400 add up to 14, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 26 steps to reach 1.
LaTeX source of the formulas on this page
\[ 46400 = 2^{6} \times 5^{2} \times 29 \]46400 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 42 |
| Sum of divisors | 118110 |
| Euler totient φ(n) | 17920 |
| Square | 2152960000 |
| Cube | 99897344000000 |
| Square root | 215.406592 (= 40√29) |
| Digit sum / digital root | 14 / 5 |
| Collatz steps to 1 | 26 |
| Scientific notation | 4.64 × |
46400 in other forms
| Form | Value |
|---|---|
| In words | forty-six thousand four hundred |
| Binary (base 2) | 1011010101000000 |
| Octal (base 8) | 132500 |
| Hexadecimal (base 16) | B540 |
| Base 3 | 2100122112 |
| As time | 46400 seconds = 12 h 53 min 20 s |
Is 46400 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (46400 ÷ 2 = 23200) | 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 (46400 ÷ 4 = 11600) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (46400 ÷ 5 = 9280) | 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 | No (remainder 4) | 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 (46400 ÷ 8 = 5800) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 5) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (46400 ÷ 10 = 4640) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 2) | 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 46400 a prime number?
No. 46400 = × × 29, so it is divisible by 2.
What are the factors of 46400?
1, 2, 4, 5, 8, 10, 16, 20, 25, 29, 32, 40, 50, 58, 64, 80, 100, 116, 145, 160, 200, 232, 290, 320, 400, 464, 580, 725, 800, 928, 1160, 1450, 1600, 1856, 2320, 2900, 4640, 5800, 9280, 11600, 23200, 46400.
What is 46400 in binary?
1011010101000000 (hexadecimal B540, octal 132500).
What is the square root of 46400?
About 215.4066, exactly 40√29.
Is 46400 divisible by 3?
No. Its digits add up to 14, which is not a multiple of 3.
What is special about the number 46400?
46400 is a happy number: repeatedly adding the squares of its digits reaches 1.