The number 441
441 is a perfect square (21²). Its prime factorisation is × . Divisors (9): 1, 3, 7, 9, 21, 49, 63, 147, 441.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 441: a perfect square (21²); a Harshad number: divisible by its digit sum 9.
- 2
441 is composite. Its prime factorisation is
- 3
The divisors add up to 741; without 441 itself that is 300, so 441 is deficient (300 is less than 441). Euler's totient φ(441) = 252 numbers up to 441 share no factor with it.
- 4
The digits of 441 add up to 9, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 27 steps to reach 1.
LaTeX source of the formulas on this page
\[ 441 = 3^{2} \times 7^{2} \]441 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 9 |
| Sum of divisors | 741 |
| Euler totient φ(n) | 252 |
| Square | 194481 |
| Cube | 85766121 |
| Square root | 21 |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 27 |
| Scientific notation | 4.41 × |
| Perfect power |
441 in other forms
| Form | Value |
|---|---|
| In words | four hundred and forty-one |
| Roman numerals | CDXLI |
| Binary (base 2) | 110111001 |
| Octal (base 8) | 671 |
| Hexadecimal (base 16) | 1B9 |
| Base 3 | 121100 |
| As time | 441 seconds = 7 min 21 s |
Is 441 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | No (remainder 1) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (441 ÷ 3 = 147) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 1) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 1) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 3) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (441 ÷ 7 = 63) | 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 1) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (441 ÷ 9 = 49) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 1) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 9) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 441 a prime number?
No. 441 = × , so it is divisible by 3.
What are the factors of 441?
1, 3, 7, 9, 21, 49, 63, 147, 441.
What is 441 in binary?
110111001 (hexadecimal 1B9, octal 671).
What is the square root of 441?
21, because 21 × 21 = 441.
What is 441 in Roman numerals?
CDXLI.
Is 441 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 441?
441 is a perfect square (21²); a Harshad number: divisible by its digit sum 9.