The number 5940
5940 is a composite number with 48 divisors. Its prime factorisation is × × 5 × 11. Divisors (48): 1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 15, 18, 20, 22, 27, 30 … 5940.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 5940: a Harshad number: divisible by its digit sum 18.
- 2
5940 is composite. Its prime factorisation is
- 3
The divisors add up to 20160; without 5940 itself that is 14220, so 5940 is abundant (14220 is more than 5940). Euler's totient φ(5940) = 1440 numbers up to 5940 share no factor with it.
- 4
The digits of 5940 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 49 steps to reach 1.
LaTeX source of the formulas on this page
\[ 5940 = 2^{2} \times 3^{3} \times 5 \times 11 \]5940 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 20160 |
| Euler totient φ(n) | 1440 |
| Square | 35283600 |
| Cube | 209584584000 |
| Square root | 77.071395 (= 6√165) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 49 |
| Scientific notation | 5.94 × |
5940 in other forms
| Form | Value |
|---|---|
| In words | five thousand nine hundred and forty |
| Binary (base 2) | 1011100110100 |
| Octal (base 8) | 13464 |
| Hexadecimal (base 16) | 1734 |
| Base 3 | 22011000 |
| As time | 5940 seconds = 1 h 39 min 0 s |
Is 5940 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (5940 ÷ 2 = 2970) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (5940 ÷ 3 = 1980) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (5940 ÷ 4 = 1485) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (5940 ÷ 5 = 1188) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (5940 ÷ 6 = 990) | 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 | No (remainder 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (5940 ÷ 9 = 660) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (5940 ÷ 10 = 594) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (5940 ÷ 11 = 540) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (5940 ÷ 12 = 495) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 5940 a prime number?
No. 5940 = × × 5 × 11, so it is divisible by 2.
What are the factors of 5940?
1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 15, 18, 20, 22, 27, 30, 33, 36, 44, 45, 54, 55, 60, 66, 90, 99, 108, 110, 132, 135, 165, 180, 198, 220, 270, 297, 330, 396, 495, 540, 594, 660, 990, 1188, 1485, 1980, 2970, 5940.
What is 5940 in binary?
1011100110100 (hexadecimal 1734, octal 13464).
What is the square root of 5940?
About 77.0714, exactly 6√165.
Is 5940 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 5940?
5940 is a Harshad number: divisible by its digit sum 18.