The number 39960
39960 is a composite number with 64 divisors. Its prime factorisation is × × 5 × 37. Divisors (64): 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 27, 30 … 39960.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 39960: a Harshad number: divisible by its digit sum 27.
- 2
39960 is composite. Its prime factorisation is
- 3
The divisors add up to 136800; without 39960 itself that is 96840, so 39960 is abundant (96840 is more than 39960). Euler's totient φ(39960) = 10368 numbers up to 39960 share no factor with it.
- 4
The digits of 39960 add up to 27, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 93 steps to reach 1.
LaTeX source of the formulas on this page
\[ 39960 = 2^{3} \times 3^{3} \times 5 \times 37 \]39960 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 64 |
| Sum of divisors | 136800 |
| Euler totient φ(n) | 10368 |
| Square | 1596801600 |
| Cube | 63808191936000 |
| Square root | 199.899975 (= 6√1110) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 93 |
| Scientific notation | 3.996 × |
39960 in other forms
| Form | Value |
|---|---|
| In words | thirty-nine thousand nine hundred and sixty |
| Binary (base 2) | 1001110000011000 |
| Octal (base 8) | 116030 |
| Hexadecimal (base 16) | 9C18 |
| Base 3 | 2000211000 |
| As time | 39960 seconds = 11 h 6 min 0 s |
Is 39960 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (39960 ÷ 2 = 19980) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (39960 ÷ 3 = 13320) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (39960 ÷ 4 = 9990) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (39960 ÷ 5 = 7992) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (39960 ÷ 6 = 6660) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 (39960 ÷ 8 = 4995) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (39960 ÷ 9 = 4440) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (39960 ÷ 10 = 3996) | 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 (39960 ÷ 12 = 3330) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 39960 a prime number?
No. 39960 = × × 5 × 37, so it is divisible by 2.
What are the factors of 39960?
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 27, 30, 36, 37, 40, 45, 54, 60, 72, 74, 90, 108, 111, 120, 135, 148, 180, 185, 216, 222, 270, 296, 333, 360, 370, 444, 540, 555, 666, 740, 888, 999, 1080, 1110, 1332, 1480, 1665, 1998, 2220, 2664, 3330, 3996, 4440, 4995, 6660, 7992, 9990, 13320, 19980, 39960.
What is 39960 in binary?
1001110000011000 (hexadecimal 9C18, octal 116030).
What is the square root of 39960?
About 199.9000, exactly 6√1110.
Is 39960 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 39960?
39960 is a Harshad number: divisible by its digit sum 27.