The number 3680
3680 is a composite number with 24 divisors. Its prime factorisation is × 5 × 23. Divisors (24): 1, 2, 4, 5, 8, 10, 16, 20, 23, 32, 40, 46, 80, 92, 115, 160 … 3680.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 3680: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
3680 is composite. Its prime factorisation is
- 3
The divisors add up to 9072; without 3680 itself that is 5392, so 3680 is abundant (5392 is more than 3680). Euler's totient φ(3680) = 1408 numbers up to 3680 share no factor with it.
- 4
The digits of 3680 add up to 17, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 38 steps to reach 1.
LaTeX source of the formulas on this page
\[ 3680 = 2^{5} \times 5 \times 23 \]3680 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 9072 |
| Euler totient φ(n) | 1408 |
| Square | 13542400 |
| Cube | 49836032000 |
| Square root | 60.663004 (= 4√230) |
| Digit sum / digital root | 17 / 8 |
| Collatz steps to 1 | 38 |
| Scientific notation | 3.68 × |
3680 in other forms
| Form | Value |
|---|---|
| In words | three thousand six hundred and eighty |
| Roman numerals | MMMDCLXXX |
| Binary (base 2) | 111001100000 |
| Octal (base 8) | 7140 |
| Hexadecimal (base 16) | E60 |
| Base 3 | 12001022 |
| As time | 3680 seconds = 1 h 1 min 20 s |
Is 3680 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (3680 ÷ 2 = 1840) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (3680 ÷ 4 = 920) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (3680 ÷ 5 = 736) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 2) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 (3680 ÷ 8 = 460) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 8) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (3680 ÷ 10 = 368) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 3680 a prime number?
No. 3680 = × 5 × 23, so it is divisible by 2.
What are the factors of 3680?
1, 2, 4, 5, 8, 10, 16, 20, 23, 32, 40, 46, 80, 92, 115, 160, 184, 230, 368, 460, 736, 920, 1840, 3680.
What is 3680 in binary?
111001100000 (hexadecimal E60, octal 7140).
What is the square root of 3680?
About 60.6630, exactly 4√230.
What is 3680 in Roman numerals?
MMMDCLXXX.
Is 3680 divisible by 3?
No. Its digits add up to 17, which is not a multiple of 3.
What is special about the number 3680?
3680 is a happy number: repeatedly adding the squares of its digits reaches 1.