The number 34800
34800 is a composite number with 60 divisors. Its prime factorisation is × 3 × × 29. Divisors (60): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 29, 30 … 34800.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 34800: a Harshad number: divisible by its digit sum 15.
- 2
34800 is composite. Its prime factorisation is
- 3
The divisors add up to 115320; without 34800 itself that is 80520, so 34800 is abundant (80520 is more than 34800). Euler's totient φ(34800) = 8960 numbers up to 34800 share no factor with it.
- 4
The digits of 34800 add up to 15, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 80 steps to reach 1.
LaTeX source of the formulas on this page
\[ 34800 = 2^{4} \times 3 \times 5^{2} \times 29 \]34800 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 60 |
| Sum of divisors | 115320 |
| Euler totient φ(n) | 8960 |
| Square | 1211040000 |
| Cube | 42144192000000 |
| Square root | 186.547581 (= 20√87) |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 80 |
| Scientific notation | 3.48 × |
34800 in other forms
| Form | Value |
|---|---|
| In words | thirty-four thousand eight hundred |
| Binary (base 2) | 1000011111110000 |
| Octal (base 8) | 103760 |
| Hexadecimal (base 16) | 87F0 |
| Base 3 | 1202201220 |
| As time | 34800 seconds = 9 h 40 min 0 s |
Is 34800 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (34800 ÷ 2 = 17400) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (34800 ÷ 3 = 11600) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (34800 ÷ 4 = 8700) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (34800 ÷ 5 = 6960) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (34800 ÷ 6 = 5800) | 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 | Yes (34800 ÷ 8 = 4350) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (34800 ÷ 10 = 3480) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 7) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (34800 ÷ 12 = 2900) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 34800 a prime number?
No. 34800 = × 3 × × 29, so it is divisible by 2.
What are the factors of 34800?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 29, 30, 40, 48, 50, 58, 60, 75, 80, 87, 100, 116, 120, 145, 150, 174, 200, 232, 240, 290, 300, 348, 400, 435, 464, 580, 600, 696, 725, 870, 1160, 1200, 1392, 1450, 1740, 2175, 2320, 2900, 3480, 4350, 5800, 6960, 8700, 11600, 17400, 34800.
What is 34800 in binary?
1000011111110000 (hexadecimal 87F0, octal 103760).
What is the square root of 34800?
About 186.5476, exactly 20√87.
Is 34800 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 34800?
34800 is a Harshad number: divisible by its digit sum 15.