The number 93840
93840 is a composite number with 80 divisors. Its prime factorisation is × 3 × 5 × 17 × 23. Divisors (80): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 17, 20, 23, 24, 30 … 93840.
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How to work it out
- 1
What is special about 93840: a Harshad number: divisible by its digit sum 24.
- 2
93840 is composite. Its prime factorisation is
- 3
The divisors add up to 321408; without 93840 itself that is 227568, so 93840 is abundant (227568 is more than 93840). Euler's totient φ(93840) = 22528 numbers up to 93840 share no factor with it.
- 4
The digits of 93840 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 107 steps to reach 1.
LaTeX source of the formulas on this page
\[ 93840 = 2^{4} \times 3 \times 5 \times 17 \times 23 \]93840 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 80 |
| Sum of divisors | 321408 |
| Euler totient φ(n) | 22528 |
| Square | 8805945600 |
| Cube | 826349935104000 |
| Square root | 306.333152 (= 4√5865) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 107 |
| Scientific notation | 9.384 × |
93840 in other forms
| Form | Value |
|---|---|
| In words | ninety-three thousand eight hundred and forty |
| Binary (base 2) | 10110111010010000 |
| Octal (base 8) | 267220 |
| Hexadecimal (base 16) | 16E90 |
| Base 3 | 11202201120 |
| As time | 93840 seconds = 26 h 4 min 0 s |
Is 93840 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (93840 ÷ 2 = 46920) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (93840 ÷ 3 = 31280) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (93840 ÷ 4 = 23460) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (93840 ÷ 5 = 18768) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (93840 ÷ 6 = 15640) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 (93840 ÷ 8 = 11730) | 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 (93840 ÷ 10 = 9384) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 10) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (93840 ÷ 12 = 7820) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 93840 a prime number?
No. 93840 = × 3 × 5 × 17 × 23, so it is divisible by 2.
What are the factors of 93840?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 17, 20, 23, 24, 30, 34, 40, 46, 48, 51, 60, 68, 69, 80, 85, 92, 102, 115, 120, 136, 138, 170, 184, 204, 230, 240, 255, 272, 276, 340, 345, 368, 391, 408, 460, 510, 552, 680, 690, 782, 816, 920, 1020, 1104, 1173, 1360, 1380, 1564, 1840, 1955, 2040, 2346, 2760, 3128, 3910, 4080, 4692, 5520, 5865, 6256, 7820, 9384, 11730, 15640, 18768, 23460, 31280, 46920, 93840.
What is 93840 in binary?
10110111010010000 (hexadecimal 16E90, octal 267220).
What is the square root of 93840?
About 306.3332, exactly 4√5865.
Is 93840 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 93840?
93840 is a Harshad number: divisible by its digit sum 24.