The number 34980
34980 is a triangular number: 1 + 2 + … + 264 = 34980. Its prime factorisation is × 3 × 5 × 11 × 53. Divisors (48): 1, 2, 3, 4, 5, 6, 10, 11, 12, 15, 20, 22, 30, 33, 44, 53 … 34980.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 34980: a triangular number: 1 + 2 + … + 264 = 34980.
- 2
34980 is composite. Its prime factorisation is
- 3
The divisors add up to 108864; without 34980 itself that is 73884, so 34980 is abundant (73884 is more than 34980). Euler's totient φ(34980) = 8320 numbers up to 34980 share no factor with it.
- 4
The digits of 34980 add up to 24, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 54 steps to reach 1.
LaTeX source of the formulas on this page
\[ 34980 = 2^{2} \times 3 \times 5 \times 11 \times 53 \]34980 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 108864 |
| Euler totient φ(n) | 8320 |
| Square | 1223600400 |
| Cube | 42801541992000 |
| Square root | 187.029409 (= 2√8745) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 54 |
| Scientific notation | 3.498 × |
34980 in other forms
| Form | Value |
|---|---|
| In words | thirty-four thousand nine hundred and eighty |
| Binary (base 2) | 1000100010100100 |
| Octal (base 8) | 104244 |
| Hexadecimal (base 16) | 88A4 |
| Base 3 | 1202222120 |
| As time | 34980 seconds = 9 h 43 min 0 s |
Is 34980 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (34980 ÷ 2 = 17490) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (34980 ÷ 3 = 11660) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (34980 ÷ 4 = 8745) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (34980 ÷ 5 = 6996) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (34980 ÷ 6 = 5830) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 1) | 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 4) | 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 (34980 ÷ 10 = 3498) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (34980 ÷ 11 = 3180) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (34980 ÷ 12 = 2915) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 34980 a prime number?
No. 34980 = × 3 × 5 × 11 × 53, so it is divisible by 2.
What are the factors of 34980?
1, 2, 3, 4, 5, 6, 10, 11, 12, 15, 20, 22, 30, 33, 44, 53, 55, 60, 66, 106, 110, 132, 159, 165, 212, 220, 265, 318, 330, 530, 583, 636, 660, 795, 1060, 1166, 1590, 1749, 2332, 2915, 3180, 3498, 5830, 6996, 8745, 11660, 17490, 34980.
What is 34980 in binary?
1000100010100100 (hexadecimal 88A4, octal 104244).
What is the square root of 34980?
About 187.0294, exactly 2√8745.
Is 34980 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 34980?
34980 is a triangular number: 1 + 2 + … + 264 = 34980.