The number 3400
3400 is a composite number with 24 divisors. Its prime factorisation is × × 17. Divisors (24): 1, 2, 4, 5, 8, 10, 17, 20, 25, 34, 40, 50, 68, 85, 100, 136 … 3400.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
3400 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
3400 is composite. Its prime factorisation is
- 3
The divisors add up to 8370; without 3400 itself that is 4970, so 3400 is abundant (4970 is more than 3400). Euler's totient φ(3400) = 1280 numbers up to 3400 share no factor with it.
- 4
The digits of 3400 add up to 7, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 61 steps to reach 1.
LaTeX source of the formulas on this page
\[ 3400 = 2^{3} \times 5^{2} \times 17 \]3400 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 8370 |
| Euler totient φ(n) | 1280 |
| Square | 11560000 |
| Cube | 39304000000 |
| Square root | 58.309519 (= 10√34) |
| Digit sum / digital root | 7 / 7 |
| Collatz steps to 1 | 61 |
| Scientific notation | 3.4 × |
3400 in other forms
| Form | Value |
|---|---|
| In words | three thousand four hundred |
| Roman numerals | MMMCD |
| Binary (base 2) | 110101001000 |
| Octal (base 8) | 6510 |
| Hexadecimal (base 16) | D48 |
| Base 3 | 11122221 |
| As time | 3400 seconds = 56 min 40 s |
Is 3400 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (3400 ÷ 2 = 1700) | 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 (3400 ÷ 4 = 850) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (3400 ÷ 5 = 680) | 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 5) | 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 (3400 ÷ 8 = 425) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 7) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (3400 ÷ 10 = 340) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 1) | 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 3400 a prime number?
No. 3400 = × × 17, so it is divisible by 2.
What are the factors of 3400?
1, 2, 4, 5, 8, 10, 17, 20, 25, 34, 40, 50, 68, 85, 100, 136, 170, 200, 340, 425, 680, 850, 1700, 3400.
What is 3400 in binary?
110101001000 (hexadecimal D48, octal 6510).
What is the square root of 3400?
About 58.3095, exactly 10√34.
What is 3400 in Roman numerals?
MMMCD.
Is 3400 divisible by 3?
No. Its digits add up to 7, which is not a multiple of 3.
What is special about the number 3400?
It is a composite number with 24 divisors.