The number 660
660 is a composite number with 24 divisors. Its prime factorisation is × 3 × 5 × 11. Divisors (24): 1, 2, 3, 4, 5, 6, 10, 11, 12, 15, 20, 22, 30, 33, 44, 55 … 660.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 660: a Harshad number: divisible by its digit sum 12.
- 2
660 is composite. Its prime factorisation is
- 3
The divisors add up to 2016; without 660 itself that is 1356, so 660 is abundant (1356 is more than 660). Euler's totient φ(660) = 160 numbers up to 660 share no factor with it.
- 4
The digits of 660 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 113 steps to reach 1.
LaTeX source of the formulas on this page
\[ 660 = 2^{2} \times 3 \times 5 \times 11 \]660 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 2016 |
| Euler totient φ(n) | 160 |
| Square | 435600 |
| Cube | 287496000 |
| Square root | 25.690465 (= 2√165) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 113 |
| Scientific notation | 6.6 × |
660 in other forms
| Form | Value |
|---|---|
| In words | six hundred and sixty |
| Roman numerals | DCLX |
| Binary (base 2) | 1010010100 |
| Octal (base 8) | 1224 |
| Hexadecimal (base 16) | 294 |
| Base 3 | 220110 |
| As time | 660 seconds = 11 min 0 s |
Is 660 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (660 ÷ 2 = 330) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (660 ÷ 3 = 220) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (660 ÷ 4 = 165) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (660 ÷ 5 = 132) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (660 ÷ 6 = 110) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 (660 ÷ 10 = 66) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (660 ÷ 11 = 60) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (660 ÷ 12 = 55) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 660 a prime number?
No. 660 = × 3 × 5 × 11, so it is divisible by 2.
What are the factors of 660?
1, 2, 3, 4, 5, 6, 10, 11, 12, 15, 20, 22, 30, 33, 44, 55, 60, 66, 110, 132, 165, 220, 330, 660.
What is 660 in binary?
1010010100 (hexadecimal 294, octal 1224).
What is the square root of 660?
About 25.6905, exactly 2√165.
What is 660 in Roman numerals?
DCLX.
Is 660 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 660?
660 is a Harshad number: divisible by its digit sum 12.