The number 34140
34140 is a composite number with 24 divisors. Its prime factorisation is × 3 × 5 × 569. Divisors (24): 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 569, 1138, 1707, 2276 … 34140.
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How to work it out
- 1
What is special about 34140: a Harshad number: divisible by its digit sum 12.
- 2
34140 is composite. Its prime factorisation is
- 3
The divisors add up to 95760; without 34140 itself that is 61620, so 34140 is abundant (61620 is more than 34140). Euler's totient φ(34140) = 9088 numbers up to 34140 share no factor with it.
- 4
The digits of 34140 add up to 12, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 129 steps to reach 1.
LaTeX source of the formulas on this page
\[ 34140 = 2^{2} \times 3 \times 5 \times 569 \]34140 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 95760 |
| Euler totient φ(n) | 9088 |
| Square | 1165539600 |
| Cube | 39791521944000 |
| Square root | 184.770127 (= 2√8535) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 129 |
| Scientific notation | 3.414 × |
34140 in other forms
| Form | Value |
|---|---|
| In words | thirty-four thousand one hundred and forty |
| Binary (base 2) | 1000010101011100 |
| Octal (base 8) | 102534 |
| Hexadecimal (base 16) | 855C |
| Base 3 | 1201211110 |
| As time | 34140 seconds = 9 h 29 min 0 s |
Is 34140 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (34140 ÷ 2 = 17070) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (34140 ÷ 3 = 11380) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (34140 ÷ 4 = 8535) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (34140 ÷ 5 = 6828) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (34140 ÷ 6 = 5690) | 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 3) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (34140 ÷ 10 = 3414) | 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 (34140 ÷ 12 = 2845) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 34140 a prime number?
No. 34140 = × 3 × 5 × 569, so it is divisible by 2.
What are the factors of 34140?
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 569, 1138, 1707, 2276, 2845, 3414, 5690, 6828, 8535, 11380, 17070, 34140.
What is 34140 in binary?
1000010101011100 (hexadecimal 855C, octal 102534).
What is the square root of 34140?
About 184.7701, exactly 2√8535.
Is 34140 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 34140?
34140 is a Harshad number: divisible by its digit sum 12.