The number 1980
1980 is a composite number with 36 divisors. Its prime factorisation is × × 5 × 11. Divisors (36): 1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 15, 18, 20, 22, 30, 33 … 1980.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1980: a Harshad number: divisible by its digit sum 18.
- 2
1980 is composite. Its prime factorisation is
- 3
The divisors add up to 6552; without 1980 itself that is 4572, so 1980 is abundant (4572 is more than 1980). Euler's totient φ(1980) = 480 numbers up to 1980 share no factor with it.
- 4
The digits of 1980 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 99 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1980 = 2^{2} \times 3^{2} \times 5 \times 11 \]1980 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 6552 |
| Euler totient φ(n) | 480 |
| Square | 3920400 |
| Cube | 7762392000 |
| Square root | 44.497191 (= 6√55) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 99 |
| Scientific notation | 1.98 × |
1980 in other forms
| Form | Value |
|---|---|
| In words | one thousand nine hundred and eighty |
| Roman numerals | MCMLXXX |
| Binary (base 2) | 11110111100 |
| Octal (base 8) | 3674 |
| Hexadecimal (base 16) | 7BC |
| Base 3 | 2201100 |
| As time | 1980 seconds = 33 min 0 s |
Is 1980 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (1980 ÷ 2 = 990) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (1980 ÷ 3 = 660) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (1980 ÷ 4 = 495) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (1980 ÷ 5 = 396) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (1980 ÷ 6 = 330) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | 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 (1980 ÷ 9 = 220) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (1980 ÷ 10 = 198) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (1980 ÷ 11 = 180) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (1980 ÷ 12 = 165) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1980 a prime number?
No. 1980 = × × 5 × 11, so it is divisible by 2.
What are the factors of 1980?
1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 15, 18, 20, 22, 30, 33, 36, 44, 45, 55, 60, 66, 90, 99, 110, 132, 165, 180, 198, 220, 330, 396, 495, 660, 990, 1980.
What is 1980 in binary?
11110111100 (hexadecimal 7BC, octal 3674).
What is the square root of 1980?
About 44.4972, exactly 6√55.
What is 1980 in Roman numerals?
MCMLXXX.
Is 1980 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 1980?
1980 is a Harshad number: divisible by its digit sum 18.