The number 1680
1680 is a highly composite number: it has 40 divisors, more than any smaller number. Its prime factorisation is × 3 × 5 × 7. Divisors (40): 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24 … 1680.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1680: a highly composite number: it has 40 divisors, more than any smaller number; a Harshad number: divisible by its digit sum 15.
- 2
1680 is composite. Its prime factorisation is
- 3
The divisors add up to 5952; without 1680 itself that is 4272, so 1680 is abundant (4272 is more than 1680). Euler's totient φ(1680) = 384 numbers up to 1680 share no factor with it.
- 4
The digits of 1680 add up to 15, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 42 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1680 = 2^{4} \times 3 \times 5 \times 7 \]1680 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 40 |
| Sum of divisors | 5952 |
| Euler totient φ(n) | 384 |
| Square | 2822400 |
| Cube | 4741632000 |
| Square root | 40.987803 (= 4√105) |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 42 |
| Scientific notation | 1.68 × |
1680 in other forms
| Form | Value |
|---|---|
| In words | one thousand six hundred and eighty |
| Roman numerals | MDCLXXX |
| Binary (base 2) | 11010010000 |
| Octal (base 8) | 3220 |
| Hexadecimal (base 16) | 690 |
| Base 3 | 2022020 |
| As time | 1680 seconds = 28 min 0 s |
Is 1680 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (1680 ÷ 2 = 840) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (1680 ÷ 3 = 560) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (1680 ÷ 4 = 420) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (1680 ÷ 5 = 336) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (1680 ÷ 6 = 280) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (1680 ÷ 7 = 240) | 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 (1680 ÷ 8 = 210) | 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 (1680 ÷ 10 = 168) | 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 (1680 ÷ 12 = 140) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1680 a prime number?
No. 1680 = × 3 × 5 × 7, so it is divisible by 2.
What are the factors of 1680?
1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 28, 30, 35, 40, 42, 48, 56, 60, 70, 80, 84, 105, 112, 120, 140, 168, 210, 240, 280, 336, 420, 560, 840, 1680.
What is 1680 in binary?
11010010000 (hexadecimal 690, octal 3220).
What is the square root of 1680?
About 40.9878, exactly 4√105.
What is 1680 in Roman numerals?
MDCLXXX.
Is 1680 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 1680?
1680 is a highly composite number: it has 40 divisors, more than any smaller number; a Harshad number: divisible by its digit sum 15.