The number 34400
34400 is a composite number with 36 divisors. Its prime factorisation is × × 43. Divisors (36): 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 43, 50, 80, 86, 100 … 34400.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
34400 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
34400 is composite. Its prime factorisation is
- 3
The divisors add up to 85932; without 34400 itself that is 51532, so 34400 is abundant (51532 is more than 34400). Euler's totient φ(34400) = 13440 numbers up to 34400 share no factor with it.
- 4
The digits of 34400 add up to 11, and repeating that until one digit is left gives the digital root 2. The Collatz sequence (halve if even, else 3n+1) takes 28 steps to reach 1.
LaTeX source of the formulas on this page
\[ 34400 = 2^{5} \times 5^{2} \times 43 \]34400 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 85932 |
| Euler totient φ(n) | 13440 |
| Square | 1183360000 |
| Cube | 40707584000000 |
| Square root | 185.472370 (= 20√86) |
| Digit sum / digital root | 11 / 2 |
| Collatz steps to 1 | 28 |
| Scientific notation | 3.44 × |
34400 in other forms
| Form | Value |
|---|---|
| In words | thirty-four thousand four hundred |
| Binary (base 2) | 1000011001100000 |
| Octal (base 8) | 103140 |
| Hexadecimal (base 16) | 8660 |
| Base 3 | 1202012002 |
| As time | 34400 seconds = 9 h 33 min 20 s |
Is 34400 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (34400 ÷ 2 = 17200) | 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 (34400 ÷ 4 = 8600) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (34400 ÷ 5 = 6880) | 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 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 (34400 ÷ 8 = 4300) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 2) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (34400 ÷ 10 = 3440) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 3) | 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 34400 a prime number?
No. 34400 = × × 43, so it is divisible by 2.
What are the factors of 34400?
1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 43, 50, 80, 86, 100, 160, 172, 200, 215, 344, 400, 430, 688, 800, 860, 1075, 1376, 1720, 2150, 3440, 4300, 6880, 8600, 17200, 34400.
What is 34400 in binary?
1000011001100000 (hexadecimal 8660, octal 103140).
What is the square root of 34400?
About 185.4724, exactly 20√86.
Is 34400 divisible by 3?
No. Its digits add up to 11, which is not a multiple of 3.
What is special about the number 34400?
It is a composite number with 36 divisors.