The number 10478
10478 is a composite number with 12 divisors. Its prime factorisation is 2 × × 31. Divisors (12): 1, 2, 13, 26, 31, 62, 169, 338, 403, 806, 5239, 10478.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 10478: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
10478 is composite. Its prime factorisation is
- 3
The divisors add up to 17568; without 10478 itself that is 7090, so 10478 is deficient (7090 is less than 10478). Euler's totient φ(10478) = 4680 numbers up to 10478 share no factor with it.
- 4
The digits of 10478 add up to 20, and repeating that until one digit is left gives the digital root 2. The Collatz sequence (halve if even, else 3n+1) takes 104 steps to reach 1.
LaTeX source of the formulas on this page
\[ 10478 = 2 \times 13^{2} \times 31 \]10478 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 17568 |
| Euler totient φ(n) | 4680 |
| Square | 109788484 |
| Cube | 1150363735352 |
| Square root | 102.362102 (= 13√62) |
| Digit sum / digital root | 20 / 2 |
| Collatz steps to 1 | 104 |
| Scientific notation | 1.0478 × |
10478 in other forms
| Form | Value |
|---|---|
| In words | ten thousand four hundred and seventy-eight |
| Binary (base 2) | 10100011101110 |
| Octal (base 8) | 24356 |
| Hexadecimal (base 16) | 28EE |
| Base 3 | 112101002 |
| As time | 10478 seconds = 2 h 54 min 38 s |
Is 10478 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (10478 ÷ 2 = 5239) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 2) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 3) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 2) | 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 6) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 2) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 8) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 2) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 10478 a prime number?
No. 10478 = 2 × × 31, so it is divisible by 2.
What are the factors of 10478?
1, 2, 13, 26, 31, 62, 169, 338, 403, 806, 5239, 10478.
What is 10478 in binary?
10100011101110 (hexadecimal 28EE, octal 24356).
What is the square root of 10478?
About 102.3621, exactly 13√62.
Is 10478 divisible by 3?
No. Its digits add up to 20, which is not a multiple of 3.
What is special about the number 10478?
10478 is a happy number: repeatedly adding the squares of its digits reaches 1.