The number 34020
34020 is a composite number with 72 divisors. Its prime factorisation is × × 5 × 7. Divisors (72): 1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 27 … 34020.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 34020: a Harshad number: divisible by its digit sum 9.
- 2
34020 is composite. Its prime factorisation is
- 3
The divisors add up to 122304; without 34020 itself that is 88284, so 34020 is abundant (88284 is more than 34020). Euler's totient φ(34020) = 7776 numbers up to 34020 share no factor with it.
- 4
The digits of 34020 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 85 steps to reach 1.
LaTeX source of the formulas on this page
\[ 34020 = 2^{2} \times 3^{5} \times 5 \times 7 \]34020 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 72 |
| Sum of divisors | 122304 |
| Euler totient φ(n) | 7776 |
| Square | 1157360400 |
| Cube | 39373400808000 |
| Square root | 184.445114 (= 18√105) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 85 |
| Scientific notation | 3.402 × |
34020 in other forms
| Form | Value |
|---|---|
| In words | thirty-four thousand and twenty |
| Binary (base 2) | 1000010011100100 |
| Octal (base 8) | 102344 |
| Hexadecimal (base 16) | 84E4 |
| Base 3 | 1201200000 |
| As time | 34020 seconds = 9 h 27 min 0 s |
Is 34020 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (34020 ÷ 2 = 17010) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (34020 ÷ 3 = 11340) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (34020 ÷ 4 = 8505) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (34020 ÷ 5 = 6804) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (34020 ÷ 6 = 5670) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (34020 ÷ 7 = 4860) | 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 | Yes (34020 ÷ 9 = 3780) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (34020 ÷ 10 = 3402) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 8) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (34020 ÷ 12 = 2835) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 34020 a prime number?
No. 34020 = × × 5 × 7, so it is divisible by 2.
What are the factors of 34020?
1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 27, 28, 30, 35, 36, 42, 45, 54, 60, 63, 70, 81, 84, 90, 105, 108, 126, 135, 140, 162, 180, 189, 210, 243, 252, 270, 315, 324, 378, 405, 420, 486, 540, 567, 630, 756, 810, 945, 972, 1134, 1215, 1260, 1620, 1701, 1890, 2268, 2430, 2835, 3402, 3780, 4860, 5670, 6804, 8505, 11340, 17010, 34020.
What is 34020 in binary?
1000010011100100 (hexadecimal 84E4, octal 102344).
What is the square root of 34020?
About 184.4451, exactly 18√105.
Is 34020 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 34020?
34020 is a Harshad number: divisible by its digit sum 9.