The number 10521
10521 is a composite number with 12 divisors. Its prime factorisation is × 7 × 167. Divisors (12): 1, 3, 7, 9, 21, 63, 167, 501, 1169, 1503, 3507, 10521.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 10521: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 9.
- 2
10521 is composite. Its prime factorisation is
- 3
The divisors add up to 17472; without 10521 itself that is 6951, so 10521 is deficient (6951 is less than 10521). Euler's totient φ(10521) = 5976 numbers up to 10521 share no factor with it.
- 4
The digits of 10521 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 104 steps to reach 1.
LaTeX source of the formulas on this page
\[ 10521 = 3^{2} \times 7 \times 167 \]10521 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 17472 |
| Euler totient φ(n) | 5976 |
| Square | 110691441 |
| Cube | 1164584650761 |
| Square root | 102.571926 (= 3√1169) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 104 |
| Scientific notation | 1.0521 × |
10521 in other forms
| Form | Value |
|---|---|
| In words | ten thousand five hundred and twenty-one |
| Binary (base 2) | 10100100011001 |
| Octal (base 8) | 24431 |
| Hexadecimal (base 16) | 2919 |
| Base 3 | 112102200 |
| As time | 10521 seconds = 2 h 55 min 21 s |
Is 10521 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 (10521 ÷ 3 = 3507) | 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 (10521 ÷ 7 = 1503) | 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 (10521 ÷ 9 = 1169) | 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 5) | 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 10521 a prime number?
No. 10521 = × 7 × 167, so it is divisible by 3.
What are the factors of 10521?
1, 3, 7, 9, 21, 63, 167, 501, 1169, 1503, 3507, 10521.
What is 10521 in binary?
10100100011001 (hexadecimal 2919, octal 24431).
What is the square root of 10521?
About 102.5719, exactly 3√1169.
Is 10521 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 10521?
10521 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 9.