The number 9921
9921 is a composite number with 4 divisors. Its prime factorisation is 3 × 3307. Divisors (4): 1, 3, 3307, 9921.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 9921: a happy number: repeatedly adding the squares of its digits reaches 1; a semiprime: 3 × 3307, the product of two primes.
- 2
9921 is composite. Its prime factorisation is
- 3
The divisors add up to 13232; without 9921 itself that is 3311, so 9921 is deficient (3311 is less than 9921). Euler's totient φ(9921) = 6612 numbers up to 9921 share no factor with it.
- 4
The digits of 9921 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 135 steps to reach 1.
LaTeX source of the formulas on this page
\[ 9921 = 3 \times 3307 \]
9921 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 4 |
| Sum of divisors | 13232 |
| Euler totient φ(n) | 6612 |
| Square | 98426241 |
| Cube | 976486736961 |
| Square root | 99.604217 |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 135 |
| Scientific notation | 9.921 × |
9921 in other forms
| Form | Value |
|---|---|
| In words | nine thousand nine hundred and twenty-one |
| Binary (base 2) | 10011011000001 |
| Octal (base 8) | 23301 |
| Hexadecimal (base 16) | 26C1 |
| Base 3 | 111121110 |
| As time | 9921 seconds = 2 h 45 min 21 s |
Is 9921 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 (9921 ÷ 3 = 3307) | 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 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 3) | 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 10) | 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 9921 a prime number?
No. 9921 = 3 × 3307, so it is divisible by 3.
What are the factors of 9921?
1, 3, 3307, 9921.
What is 9921 in binary?
10011011000001 (hexadecimal 26C1, octal 23301).
What is the square root of 9921?
About 99.6042.
Is 9921 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 9921?
9921 is a happy number: repeatedly adding the squares of its digits reaches 1; a semiprime: 3 × 3307, the product of two primes.