The number 3980
3980 is a composite number with 12 divisors. Its prime factorisation is × 5 × 199. Divisors (12): 1, 2, 4, 5, 10, 20, 199, 398, 796, 995, 1990, 3980.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 3980: a Harshad number: divisible by its digit sum 20.
- 2
3980 is composite. Its prime factorisation is
- 3
The divisors add up to 8400; without 3980 itself that is 4420, so 3980 is abundant (4420 is more than 3980). Euler's totient φ(3980) = 1584 numbers up to 3980 share no factor with it.
- 4
The digits of 3980 add up to 20, and repeating that until one digit is left gives the digital root 2. The Collatz sequence (halve if even, else 3n+1) takes 25 steps to reach 1.
LaTeX source of the formulas on this page
\[ 3980 = 2^{2} \times 5 \times 199 \]3980 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 8400 |
| Euler totient φ(n) | 1584 |
| Square | 15840400 |
| Cube | 63044792000 |
| Square root | 63.087241 (= 2√995) |
| Digit sum / digital root | 20 / 2 |
| Collatz steps to 1 | 25 |
| Scientific notation | 3.98 × |
3980 in other forms
| Form | Value |
|---|---|
| In words | three thousand nine hundred and eighty |
| Roman numerals | MMMCMLXXX |
| Binary (base 2) | 111110001100 |
| Octal (base 8) | 7614 |
| Hexadecimal (base 16) | F8C |
| Base 3 | 12110102 |
| As time | 3980 seconds = 1 h 6 min 20 s |
Is 3980 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (3980 ÷ 2 = 1990) | 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 (3980 ÷ 4 = 995) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (3980 ÷ 5 = 796) | 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 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 | No (remainder 2) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (3980 ÷ 10 = 398) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 9) | 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 3980 a prime number?
No. 3980 = × 5 × 199, so it is divisible by 2.
What are the factors of 3980?
1, 2, 4, 5, 10, 20, 199, 398, 796, 995, 1990, 3980.
What is 3980 in binary?
111110001100 (hexadecimal F8C, octal 7614).
What is the square root of 3980?
About 63.0872, exactly 2√995.
What is 3980 in Roman numerals?
MMMCMLXXX.
Is 3980 divisible by 3?
No. Its digits add up to 20, which is not a multiple of 3.
What is special about the number 3980?
3980 is a Harshad number: divisible by its digit sum 20.