The number 39840
39840 is a composite number with 48 divisors. Its prime factorisation is × 3 × 5 × 83. Divisors (48): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40 … 39840.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 39840: a Harshad number: divisible by its digit sum 24.
- 2
39840 is composite. Its prime factorisation is
- 3
The divisors add up to 127008; without 39840 itself that is 87168, so 39840 is abundant (87168 is more than 39840). Euler's totient φ(39840) = 10496 numbers up to 39840 share no factor with it.
- 4
The digits of 39840 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 93 steps to reach 1.
LaTeX source of the formulas on this page
\[ 39840 = 2^{5} \times 3 \times 5 \times 83 \]39840 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 127008 |
| Euler totient φ(n) | 10496 |
| Square | 1587225600 |
| Cube | 63235067904000 |
| Square root | 199.599599 (= 4√2490) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 93 |
| Scientific notation | 3.984 × |
39840 in other forms
| Form | Value |
|---|---|
| In words | thirty-nine thousand eight hundred and forty |
| Binary (base 2) | 1001101110100000 |
| Octal (base 8) | 115640 |
| Hexadecimal (base 16) | 9BA0 |
| Base 3 | 2000122120 |
| As time | 39840 seconds = 11 h 4 min 0 s |
Is 39840 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (39840 ÷ 2 = 19920) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (39840 ÷ 3 = 13280) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (39840 ÷ 4 = 9960) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (39840 ÷ 5 = 7968) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (39840 ÷ 6 = 6640) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 (39840 ÷ 8 = 4980) | 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 (39840 ÷ 10 = 3984) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 9) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (39840 ÷ 12 = 3320) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 39840 a prime number?
No. 39840 = × 3 × 5 × 83, so it is divisible by 2.
What are the factors of 39840?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 80, 83, 96, 120, 160, 166, 240, 249, 332, 415, 480, 498, 664, 830, 996, 1245, 1328, 1660, 1992, 2490, 2656, 3320, 3984, 4980, 6640, 7968, 9960, 13280, 19920, 39840.
What is 39840 in binary?
1001101110100000 (hexadecimal 9BA0, octal 115640).
What is the square root of 39840?
About 199.5996, exactly 4√2490.
Is 39840 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 39840?
39840 is a Harshad number: divisible by its digit sum 24.