The number 8424
8424 is a composite number with 40 divisors. Its prime factorisation is × × 13. Divisors (40): 1, 2, 3, 4, 6, 8, 9, 12, 13, 18, 24, 26, 27, 36, 39, 52 … 8424.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 8424: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.
- 2
8424 is composite. Its prime factorisation is
- 3
The divisors add up to 25410; without 8424 itself that is 16986, so 8424 is abundant (16986 is more than 8424). Euler's totient φ(8424) = 2592 numbers up to 8424 share no factor with it.
- 4
The digits of 8424 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 83 steps to reach 1.
LaTeX source of the formulas on this page
\[ 8424 = 2^{3} \times 3^{4} \times 13 \]8424 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 40 |
| Sum of divisors | 25410 |
| Euler totient φ(n) | 2592 |
| Square | 70963776 |
| Cube | 597798849024 |
| Square root | 91.782351 (= 18√26) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 83 |
| Scientific notation | 8.424 × |
8424 in other forms
| Form | Value |
|---|---|
| In words | eight thousand four hundred and twenty-four |
| Binary (base 2) | 10000011101000 |
| Octal (base 8) | 20350 |
| Hexadecimal (base 16) | 20E8 |
| Base 3 | 102120000 |
| As time | 8424 seconds = 2 h 20 min 24 s |
Is 8424 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (8424 ÷ 2 = 4212) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (8424 ÷ 3 = 2808) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (8424 ÷ 4 = 2106) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 4) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (8424 ÷ 6 = 1404) | 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 | Yes (8424 ÷ 8 = 1053) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (8424 ÷ 9 = 936) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 4) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 9) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (8424 ÷ 12 = 702) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 8424 a prime number?
No. 8424 = × × 13, so it is divisible by 2.
What are the factors of 8424?
1, 2, 3, 4, 6, 8, 9, 12, 13, 18, 24, 26, 27, 36, 39, 52, 54, 72, 78, 81, 104, 108, 117, 156, 162, 216, 234, 312, 324, 351, 468, 648, 702, 936, 1053, 1404, 2106, 2808, 4212, 8424.
What is 8424 in binary?
10000011101000 (hexadecimal 20E8, octal 20350).
What is the square root of 8424?
About 91.7824, exactly 18√26.
Is 8424 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 8424?
8424 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.