The number 10380
10380 is a composite number with 24 divisors. Its prime factorisation is × 3 × 5 × 173. Divisors (24): 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 173, 346, 519, 692 … 10380.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 10380: a Harshad number: divisible by its digit sum 12.
- 2
10380 is composite. Its prime factorisation is
- 3
The divisors add up to 29232; without 10380 itself that is 18852, so 10380 is abundant (18852 is more than 10380). Euler's totient φ(10380) = 2752 numbers up to 10380 share no factor with it.
- 4
The digits of 10380 add up to 12, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 104 steps to reach 1.
LaTeX source of the formulas on this page
\[ 10380 = 2^{2} \times 3 \times 5 \times 173 \]10380 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 29232 |
| Euler totient φ(n) | 2752 |
| Square | 107744400 |
| Cube | 1118386872000 |
| Square root | 101.882285 (= 2√2595) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 104 |
| Scientific notation | 1.038 × |
10380 in other forms
| Form | Value |
|---|---|
| In words | ten thousand three hundred and eighty |
| Binary (base 2) | 10100010001100 |
| Octal (base 8) | 24214 |
| Hexadecimal (base 16) | 288C |
| Base 3 | 112020110 |
| As time | 10380 seconds = 2 h 53 min 0 s |
Is 10380 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (10380 ÷ 2 = 5190) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (10380 ÷ 3 = 3460) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (10380 ÷ 4 = 2595) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (10380 ÷ 5 = 2076) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (10380 ÷ 6 = 1730) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | 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 (10380 ÷ 10 = 1038) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 7) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (10380 ÷ 12 = 865) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 10380 a prime number?
No. 10380 = × 3 × 5 × 173, so it is divisible by 2.
What are the factors of 10380?
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 173, 346, 519, 692, 865, 1038, 1730, 2076, 2595, 3460, 5190, 10380.
What is 10380 in binary?
10100010001100 (hexadecimal 288C, octal 24214).
What is the square root of 10380?
About 101.8823, exactly 2√2595.
Is 10380 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 10380?
10380 is a Harshad number: divisible by its digit sum 12.