The number 121
121 is a perfect square (11²) and a palindrome: it reads 121 backwards too. Its prime factorisation is . Divisors (3): 1, 11, 121.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 121: a perfect square (11²); a palindrome: it reads 121 backwards too; the square of a prime (11²).
- 2
121 is composite. Its prime factorisation is
- 3
The divisors add up to 133; without 121 itself that is 12, so 121 is deficient (12 is less than 121). Euler's totient φ(121) = 110 numbers up to 121 share no factor with it.
- 4
The digits of 121 add up to 4, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 95 steps to reach 1.
LaTeX source of the formulas on this page
\[ 121 = 11^{2} \]121 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 3 |
| Sum of divisors | 133 |
| Euler totient φ(n) | 110 |
| Square | 14641 |
| Cube | 1771561 |
| Square root | 11 |
| Digit sum / digital root | 4 / 4 |
| Collatz steps to 1 | 95 |
| Scientific notation | 1.21 × |
| Perfect power |
121 in other forms
| Form | Value |
|---|---|
| In words | one hundred and twenty-one |
| Roman numerals | CXXI |
| Binary (base 2) | 1111001 |
| Octal (base 8) | 171 |
| Hexadecimal (base 16) | 79 |
| Base 3 | 11111 |
| As time | 121 seconds = 2 min 1 s |
Is 121 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 | No (remainder 1) | 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 1) | 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 1) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 4) | 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 (121 ÷ 11 = 11) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 1) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 121 a prime number?
No. 121 = , so it is divisible by 11.
What are the factors of 121?
1, 11, 121.
What is 121 in binary?
1111001 (hexadecimal 79, octal 171).
What is the square root of 121?
11, because 11 × 11 = 121.
What is 121 in Roman numerals?
CXXI.
Is 121 divisible by 3?
No. Its digits add up to 4, which is not a multiple of 3.
What is special about the number 121?
121 is a perfect square (11²); a palindrome: it reads 121 backwards too; the square of a prime (11²).