The number 8724
8724 is a composite number with 12 divisors. Its prime factorisation is × 3 × 727. Divisors (12): 1, 2, 3, 4, 6, 12, 727, 1454, 2181, 2908, 4362, 8724.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 8724: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
8724 is composite. Its prime factorisation is
- 3
The divisors add up to 20384; without 8724 itself that is 11660, so 8724 is abundant (11660 is more than 8724). Euler's totient φ(8724) = 2904 numbers up to 8724 share no factor with it.
- 4
The digits of 8724 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 47 steps to reach 1.
LaTeX source of the formulas on this page
\[ 8724 = 2^{2} \times 3 \times 727 \]8724 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 20384 |
| Euler totient φ(n) | 2904 |
| Square | 76108176 |
| Cube | 663967727424 |
| Square root | 93.402355 (= 2√2181) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 47 |
| Scientific notation | 8.724 × |
8724 in other forms
| Form | Value |
|---|---|
| In words | eight thousand seven hundred and twenty-four |
| Binary (base 2) | 10001000010100 |
| Octal (base 8) | 21024 |
| Hexadecimal (base 16) | 2214 |
| Base 3 | 102222010 |
| As time | 8724 seconds = 2 h 25 min 24 s |
Is 8724 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (8724 ÷ 2 = 4362) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (8724 ÷ 3 = 2908) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (8724 ÷ 4 = 2181) | 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 (8724 ÷ 6 = 1454) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 | No (remainder 4) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (8724 ÷ 12 = 727) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 8724 a prime number?
No. 8724 = × 3 × 727, so it is divisible by 2.
What are the factors of 8724?
1, 2, 3, 4, 6, 12, 727, 1454, 2181, 2908, 4362, 8724.
What is 8724 in binary?
10001000010100 (hexadecimal 2214, octal 21024).
What is the square root of 8724?
About 93.4024, exactly 2√2181.
Is 8724 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 8724?
8724 is a happy number: repeatedly adding the squares of its digits reaches 1.