The number 19740
19740 is a composite number with 48 divisors. Its prime factorisation is × 3 × 5 × 7 × 47. Divisors (48): 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35 … 19740.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 19740: a Harshad number: divisible by its digit sum 21.
- 2
19740 is composite. Its prime factorisation is
- 3
The divisors add up to 64512; without 19740 itself that is 44772, so 19740 is abundant (44772 is more than 19740). Euler's totient φ(19740) = 4416 numbers up to 19740 share no factor with it.
- 4
The digits of 19740 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 198 steps to reach 1.
LaTeX source of the formulas on this page
\[ 19740 = 2^{2} \times 3 \times 5 \times 7 \times 47 \]19740 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 64512 |
| Euler totient φ(n) | 4416 |
| Square | 389667600 |
| Cube | 7692038424000 |
| Square root | 140.499110 (= 2√4935) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 198 |
| Scientific notation | 1.974 × |
19740 in other forms
| Form | Value |
|---|---|
| In words | nineteen thousand seven hundred and forty |
| Binary (base 2) | 100110100011100 |
| Octal (base 8) | 46434 |
| Hexadecimal (base 16) | 4D1C |
| Base 3 | 1000002010 |
| As time | 19740 seconds = 5 h 29 min 0 s |
Is 19740 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (19740 ÷ 2 = 9870) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (19740 ÷ 3 = 6580) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (19740 ÷ 4 = 4935) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (19740 ÷ 5 = 3948) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (19740 ÷ 6 = 3290) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (19740 ÷ 7 = 2820) | 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 3) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (19740 ÷ 10 = 1974) | 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 | Yes (19740 ÷ 12 = 1645) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 19740 a prime number?
No. 19740 = × 3 × 5 × 7 × 47, so it is divisible by 2.
What are the factors of 19740?
1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 47, 60, 70, 84, 94, 105, 140, 141, 188, 210, 235, 282, 329, 420, 470, 564, 658, 705, 940, 987, 1316, 1410, 1645, 1974, 2820, 3290, 3948, 4935, 6580, 9870, 19740.
What is 19740 in binary?
100110100011100 (hexadecimal 4D1C, octal 46434).
What is the square root of 19740?
About 140.4991, exactly 2√4935.
Is 19740 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 19740?
19740 is a Harshad number: divisible by its digit sum 21.