The number 1638
1638 is a composite number with 24 divisors. Its prime factorisation is 2 × × 7 × 13. Divisors (24): 1, 2, 3, 6, 7, 9, 13, 14, 18, 21, 26, 39, 42, 63, 78, 91 … 1638.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1638: a Harshad number: divisible by its digit sum 18.
- 2
1638 is composite. Its prime factorisation is
- 3
The divisors add up to 4368; without 1638 itself that is 2730, so 1638 is abundant (2730 is more than 1638). Euler's totient φ(1638) = 432 numbers up to 1638 share no factor with it.
- 4
The digits of 1638 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 42 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1638 = 2 \times 3^{2} \times 7 \times 13 \]1638 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 4368 |
| Euler totient φ(n) | 432 |
| Square | 2683044 |
| Cube | 4394826072 |
| Square root | 40.472213 (= 3√182) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 42 |
| Scientific notation | 1.638 × |
1638 in other forms
| Form | Value |
|---|---|
| In words | one thousand six hundred and thirty-eight |
| Roman numerals | MDCXXXVIII |
| Binary (base 2) | 11001100110 |
| Octal (base 8) | 3146 |
| Hexadecimal (base 16) | 666 |
| Base 3 | 2020200 |
| As time | 1638 seconds = 27 min 18 s |
Is 1638 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (1638 ÷ 2 = 819) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (1638 ÷ 3 = 546) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 2) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 3) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (1638 ÷ 6 = 273) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (1638 ÷ 7 = 234) | 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 6) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (1638 ÷ 9 = 182) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 8) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 10) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 6) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1638 a prime number?
No. 1638 = 2 × × 7 × 13, so it is divisible by 2.
What are the factors of 1638?
1, 2, 3, 6, 7, 9, 13, 14, 18, 21, 26, 39, 42, 63, 78, 91, 117, 126, 182, 234, 273, 546, 819, 1638.
What is 1638 in binary?
11001100110 (hexadecimal 666, octal 3146).
What is the square root of 1638?
About 40.4722, exactly 3√182.
What is 1638 in Roman numerals?
MDCXXXVIII.
Is 1638 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 1638?
1638 is a Harshad number: divisible by its digit sum 18.