The number 19980
19980 is a composite number with 48 divisors. Its prime factorisation is × × 5 × 37. Divisors (48): 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 37 … 19980.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 19980: a Harshad number: divisible by its digit sum 27.
- 2
19980 is composite. Its prime factorisation is
- 3
The divisors add up to 63840; without 19980 itself that is 43860, so 19980 is abundant (43860 is more than 19980). Euler's totient φ(19980) = 5184 numbers up to 19980 share no factor with it.
- 4
The digits of 19980 add up to 27, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 92 steps to reach 1.
LaTeX source of the formulas on this page
\[ 19980 = 2^{2} \times 3^{3} \times 5 \times 37 \]19980 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 63840 |
| Euler totient φ(n) | 5184 |
| Square | 399200400 |
| Cube | 7976023992000 |
| Square root | 141.350628 (= 6√555) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 92 |
| Scientific notation | 1.998 × |
19980 in other forms
| Form | Value |
|---|---|
| In words | nineteen thousand nine hundred and eighty |
| Binary (base 2) | 100111000001100 |
| Octal (base 8) | 47014 |
| Hexadecimal (base 16) | 4E0C |
| Base 3 | 1000102000 |
| As time | 19980 seconds = 5 h 33 min 0 s |
Is 19980 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (19980 ÷ 2 = 9990) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (19980 ÷ 3 = 6660) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (19980 ÷ 4 = 4995) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (19980 ÷ 5 = 3996) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (19980 ÷ 6 = 3330) | 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 | Yes (19980 ÷ 9 = 2220) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (19980 ÷ 10 = 1998) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (19980 ÷ 12 = 1665) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 19980 a prime number?
No. 19980 = × × 5 × 37, so it is divisible by 2.
What are the factors of 19980?
1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 37, 45, 54, 60, 74, 90, 108, 111, 135, 148, 180, 185, 222, 270, 333, 370, 444, 540, 555, 666, 740, 999, 1110, 1332, 1665, 1998, 2220, 3330, 3996, 4995, 6660, 9990, 19980.
What is 19980 in binary?
100111000001100 (hexadecimal 4E0C, octal 47014).
What is the square root of 19980?
About 141.3506, exactly 6√555.
Is 19980 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 19980?
19980 is a Harshad number: divisible by its digit sum 27.