The number 10120
10120 is a composite number with 32 divisors. Its prime factorisation is × 5 × 11 × 23. Divisors (32): 1, 2, 4, 5, 8, 10, 11, 20, 22, 23, 40, 44, 46, 55, 88, 92 … 10120.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 10120: a Harshad number: divisible by its digit sum 4.
- 2
10120 is composite. Its prime factorisation is
- 3
The divisors add up to 25920; without 10120 itself that is 15800, so 10120 is abundant (15800 is more than 10120). Euler's totient φ(10120) = 3520 numbers up to 10120 share no factor with it.
- 4
The digits of 10120 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 42 steps to reach 1.
LaTeX source of the formulas on this page
\[ 10120 = 2^{3} \times 5 \times 11 \times 23 \]10120 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 25920 |
| Euler totient φ(n) | 3520 |
| Square | 102414400 |
| Cube | 1036433728000 |
| Square root | 100.598211 (= 2√2530) |
| Digit sum / digital root | 4 / 4 |
| Collatz steps to 1 | 42 |
| Scientific notation | 1.012 × |
10120 in other forms
| Form | Value |
|---|---|
| In words | ten thousand one hundred and twenty |
| Binary (base 2) | 10011110001000 |
| Octal (base 8) | 23610 |
| Hexadecimal (base 16) | 2788 |
| Base 3 | 111212211 |
| As time | 10120 seconds = 2 h 48 min 40 s |
Is 10120 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (10120 ÷ 2 = 5060) | 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 | Yes (10120 ÷ 4 = 2530) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (10120 ÷ 5 = 2024) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 4) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 | Yes (10120 ÷ 8 = 1265) | 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 | Yes (10120 ÷ 10 = 1012) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (10120 ÷ 11 = 920) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 10120 a prime number?
No. 10120 = × 5 × 11 × 23, so it is divisible by 2.
What are the factors of 10120?
1, 2, 4, 5, 8, 10, 11, 20, 22, 23, 40, 44, 46, 55, 88, 92, 110, 115, 184, 220, 230, 253, 440, 460, 506, 920, 1012, 1265, 2024, 2530, 5060, 10120.
What is 10120 in binary?
10011110001000 (hexadecimal 2788, octal 23610).
What is the square root of 10120?
About 100.5982, exactly 2√2530.
Is 10120 divisible by 3?
No. Its digits add up to 4, which is not a multiple of 3.
What is special about the number 10120?
10120 is a Harshad number: divisible by its digit sum 4.