The number 34200
34200 is a composite number with 72 divisors. Its prime factorisation is × × × 19. Divisors (72): 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 19, 20, 24, 25 … 34200.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 34200: a Harshad number: divisible by its digit sum 9.
- 2
34200 is composite. Its prime factorisation is
- 3
The divisors add up to 120900; without 34200 itself that is 86700, so 34200 is abundant (86700 is more than 34200). Euler's totient φ(34200) = 8640 numbers up to 34200 share no factor with it.
- 4
The digits of 34200 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 67 steps to reach 1.
LaTeX source of the formulas on this page
\[ 34200 = 2^{3} \times 3^{2} \times 5^{2} \times 19 \]34200 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 72 |
| Sum of divisors | 120900 |
| Euler totient φ(n) | 8640 |
| Square | 1169640000 |
| Cube | 40001688000000 |
| Square root | 184.932420 (= 30√38) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 67 |
| Scientific notation | 3.42 × |
34200 in other forms
| Form | Value |
|---|---|
| In words | thirty-four thousand two hundred |
| Binary (base 2) | 1000010110011000 |
| Octal (base 8) | 102630 |
| Hexadecimal (base 16) | 8598 |
| Base 3 | 1201220200 |
| As time | 34200 seconds = 9 h 30 min 0 s |
Is 34200 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (34200 ÷ 2 = 17100) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (34200 ÷ 3 = 11400) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (34200 ÷ 4 = 8550) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (34200 ÷ 5 = 6840) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (34200 ÷ 6 = 5700) | 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 (34200 ÷ 8 = 4275) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (34200 ÷ 9 = 3800) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (34200 ÷ 10 = 3420) | 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 | Yes (34200 ÷ 12 = 2850) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 34200 a prime number?
No. 34200 = × × × 19, so it is divisible by 2.
What are the factors of 34200?
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 19, 20, 24, 25, 30, 36, 38, 40, 45, 50, 57, 60, 72, 75, 76, 90, 95, 100, 114, 120, 150, 152, 171, 180, 190, 200, 225, 228, 285, 300, 342, 360, 380, 450, 456, 475, 570, 600, 684, 760, 855, 900, 950, 1140, 1368, 1425, 1710, 1800, 1900, 2280, 2850, 3420, 3800, 4275, 5700, 6840, 8550, 11400, 17100, 34200.
What is 34200 in binary?
1000010110011000 (hexadecimal 8598, octal 102630).
What is the square root of 34200?
About 184.9324, exactly 30√38.
Is 34200 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 34200?
34200 is a Harshad number: divisible by its digit sum 9.