The number 10020
10020 is a composite number with 24 divisors. Its prime factorisation is × 3 × 5 × 167. Divisors (24): 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 167, 334, 501, 668 … 10020.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 10020: a Harshad number: divisible by its digit sum 3.
- 2
10020 is composite. Its prime factorisation is
- 3
The divisors add up to 28224; without 10020 itself that is 18204, so 10020 is abundant (18204 is more than 10020). Euler's totient φ(10020) = 2656 numbers up to 10020 share no factor with it.
- 4
The digits of 10020 add up to 3, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 91 steps to reach 1.
LaTeX source of the formulas on this page
\[ 10020 = 2^{2} \times 3 \times 5 \times 167 \]10020 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 28224 |
| Euler totient φ(n) | 2656 |
| Square | 100400400 |
| Cube | 1006012008000 |
| Square root | 100.099950 (= 2√2505) |
| Digit sum / digital root | 3 / 3 |
| Collatz steps to 1 | 91 |
| Scientific notation | 1.002 × |
10020 in other forms
| Form | Value |
|---|---|
| In words | ten thousand and twenty |
| Binary (base 2) | 10011100100100 |
| Octal (base 8) | 23444 |
| Hexadecimal (base 16) | 2724 |
| Base 3 | 111202010 |
| As time | 10020 seconds = 2 h 47 min 0 s |
Is 10020 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (10020 ÷ 2 = 5010) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (10020 ÷ 3 = 3340) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (10020 ÷ 4 = 2505) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (10020 ÷ 5 = 2004) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (10020 ÷ 6 = 1670) | 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 4) | 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 | Yes (10020 ÷ 10 = 1002) | 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 | Yes (10020 ÷ 12 = 835) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 10020 a prime number?
No. 10020 = × 3 × 5 × 167, so it is divisible by 2.
What are the factors of 10020?
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 167, 334, 501, 668, 835, 1002, 1670, 2004, 2505, 3340, 5010, 10020.
What is 10020 in binary?
10011100100100 (hexadecimal 2724, octal 23444).
What is the square root of 10020?
About 100.1000, exactly 2√2505.
Is 10020 divisible by 3?
Yes. Its digits add up to 3, a multiple of 3.
What is special about the number 10020?
10020 is a Harshad number: divisible by its digit sum 3.