The number 34080
34080 is a composite number with 48 divisors. Its prime factorisation is × 3 × 5 × 71. Divisors (48): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40 … 34080.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 34080: a Harshad number: divisible by its digit sum 15.
- 2
34080 is composite. Its prime factorisation is
- 3
The divisors add up to 108864; without 34080 itself that is 74784, so 34080 is abundant (74784 is more than 34080). Euler's totient φ(34080) = 8960 numbers up to 34080 share no factor with it.
- 4
The digits of 34080 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
\[ 34080 = 2^{5} \times 3 \times 5 \times 71 \]34080 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 108864 |
| Euler totient φ(n) | 8960 |
| Square | 1161446400 |
| Cube | 39582093312000 |
| Square root | 184.607692 (= 4√2130) |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 80 |
| Scientific notation | 3.408 × |
34080 in other forms
| Form | Value |
|---|---|
| In words | thirty-four thousand and eighty |
| Binary (base 2) | 1000010100100000 |
| Octal (base 8) | 102440 |
| Hexadecimal (base 16) | 8520 |
| Base 3 | 1201202020 |
| As time | 34080 seconds = 9 h 28 min 0 s |
Is 34080 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (34080 ÷ 2 = 17040) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (34080 ÷ 3 = 11360) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (34080 ÷ 4 = 8520) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (34080 ÷ 5 = 6816) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (34080 ÷ 6 = 5680) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 (34080 ÷ 8 = 4260) | 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 (34080 ÷ 10 = 3408) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 2) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (34080 ÷ 12 = 2840) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 34080 a prime number?
No. 34080 = × 3 × 5 × 71, so it is divisible by 2.
What are the factors of 34080?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 71, 80, 96, 120, 142, 160, 213, 240, 284, 355, 426, 480, 568, 710, 852, 1065, 1136, 1420, 1704, 2130, 2272, 2840, 3408, 4260, 5680, 6816, 8520, 11360, 17040, 34080.
What is 34080 in binary?
1000010100100000 (hexadecimal 8520, octal 102440).
What is the square root of 34080?
About 184.6077, exactly 4√2130.
Is 34080 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 34080?
34080 is a Harshad number: divisible by its digit sum 15.