The number 34002
34002 is a composite number with 12 divisors. Its prime factorisation is 2 × × 1889. Divisors (12): 1, 2, 3, 6, 9, 18, 1889, 3778, 5667, 11334, 17001, 34002.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 34002: a Harshad number: divisible by its digit sum 9.
- 2
34002 is composite. Its prime factorisation is
- 3
The divisors add up to 73710; without 34002 itself that is 39708, so 34002 is abundant (39708 is more than 34002). Euler's totient φ(34002) = 11328 numbers up to 34002 share no factor with it.
- 4
The digits of 34002 add up to 9, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 204 steps to reach 1.
LaTeX source of the formulas on this page
\[ 34002 = 2 \times 3^{2} \times 1889 \]34002 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 73710 |
| Euler totient φ(n) | 11328 |
| Square | 1156136004 |
| Cube | 39310936408008 |
| Square root | 184.396312 (= 3√3778) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 204 |
| Scientific notation | 3.4002 × |
34002 in other forms
| Form | Value |
|---|---|
| In words | thirty-four thousand and two |
| Binary (base 2) | 1000010011010010 |
| Octal (base 8) | 102322 |
| Hexadecimal (base 16) | 84D2 |
| Base 3 | 1201122100 |
| As time | 34002 seconds = 9 h 26 min 42 s |
Is 34002 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (34002 ÷ 2 = 17001) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (34002 ÷ 3 = 11334) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 2) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 2) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (34002 ÷ 6 = 5667) | 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 | No (remainder 2) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (34002 ÷ 9 = 3778) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 2) | 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 6) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 34002 a prime number?
No. 34002 = 2 × × 1889, so it is divisible by 2.
What are the factors of 34002?
1, 2, 3, 6, 9, 18, 1889, 3778, 5667, 11334, 17001, 34002.
What is 34002 in binary?
1000010011010010 (hexadecimal 84D2, octal 102322).
What is the square root of 34002?
About 184.3963, exactly 3√3778.
Is 34002 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 34002?
34002 is a Harshad number: divisible by its digit sum 9.