The number 2121
2121 is a composite number with 8 divisors. Its prime factorisation is 3 × 7 × 101. Divisors (8): 1, 3, 7, 21, 101, 303, 707, 2121.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 2121: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
2121 is composite. Its prime factorisation is
- 3
The divisors add up to 3264; without 2121 itself that is 1143, so 2121 is deficient (1143 is less than 2121). Euler's totient φ(2121) = 1200 numbers up to 2121 share no factor with it.
- 4
The digits of 2121 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 107 steps to reach 1.
LaTeX source of the formulas on this page
\[ 2121 = 3 \times 7 \times 101 \]
2121 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 8 |
| Sum of divisors | 3264 |
| Euler totient φ(n) | 1200 |
| Square | 4498641 |
| Cube | 9541617561 |
| Square root | 46.054316 |
| Digit sum / digital root | 6 / 6 |
| Collatz steps to 1 | 107 |
| Scientific notation | 2.121 × |
2121 in other forms
| Form | Value |
|---|---|
| In words | two thousand one hundred and twenty-one |
| Roman numerals | MMCXXI |
| Binary (base 2) | 100001001001 |
| Octal (base 8) | 4111 |
| Hexadecimal (base 16) | 849 |
| Base 3 | 2220120 |
| As time | 2121 seconds = 35 min 21 s |
Is 2121 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 (2121 ÷ 3 = 707) | 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 (2121 ÷ 7 = 303) | 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 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 | No (remainder 9) | 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 2121 a prime number?
No. 2121 = 3 × 7 × 101, so it is divisible by 3.
What are the factors of 2121?
1, 3, 7, 21, 101, 303, 707, 2121.
What is 2121 in binary?
100001001001 (hexadecimal 849, octal 4111).
What is the square root of 2121?
About 46.0543.
What is 2121 in Roman numerals?
MMCXXI.
Is 2121 divisible by 3?
Yes. Its digits add up to 6, a multiple of 3.
What is special about the number 2121?
2121 is a happy number: repeatedly adding the squares of its digits reaches 1.