The number 1221
1221 is a palindrome: it reads 1221 backwards too. Its prime factorisation is 3 × 11 × 37. Divisors (8): 1, 3, 11, 33, 37, 111, 407, 1221.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1221: a palindrome: it reads 1221 backwards too; a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
1221 is composite. Its prime factorisation is
- 3
The divisors add up to 1824; without 1221 itself that is 603, so 1221 is deficient (603 is less than 1221). Euler's totient φ(1221) = 720 numbers up to 1221 share no factor with it.
- 4
The digits of 1221 add up to 6, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 39 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1221 = 3 \times 11 \times 37 \]
1221 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 8 |
| Sum of divisors | 1824 |
| Euler totient φ(n) | 720 |
| Square | 1490841 |
| Cube | 1820316861 |
| Square root | 34.942810 |
| Digit sum / digital root | 6 / 6 |
| Collatz steps to 1 | 39 |
| Scientific notation | 1.221 × |
1221 in other forms
| Form | Value |
|---|---|
| In words | one thousand two hundred and twenty-one |
| Roman numerals | MCCXXI |
| Binary (base 2) | 10011000101 |
| Octal (base 8) | 2305 |
| Hexadecimal (base 16) | 4C5 |
| Base 3 | 1200020 |
| As time | 1221 seconds = 20 min 21 s |
Is 1221 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 (1221 ÷ 3 = 407) | 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 | No (remainder 3) | 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 5) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | 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 | Yes (1221 ÷ 11 = 111) | 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 1221 a prime number?
No. 1221 = 3 × 11 × 37, so it is divisible by 3.
What are the factors of 1221?
1, 3, 11, 33, 37, 111, 407, 1221.
What is 1221 in binary?
10011000101 (hexadecimal 4C5, octal 2305).
What is the square root of 1221?
About 34.9428.
What is 1221 in Roman numerals?
MCCXXI.
Is 1221 divisible by 3?
Yes. Its digits add up to 6, a multiple of 3.
What is special about the number 1221?
1221 is a palindrome: it reads 1221 backwards too; a happy number: repeatedly adding the squares of its digits reaches 1.