The number 7884
7884 is a composite number with 24 divisors. Its prime factorisation is × × 73. Divisors (24): 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 73, 108, 146, 219, 292 … 7884.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 7884: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 27.
- 2
7884 is composite. Its prime factorisation is
- 3
The divisors add up to 20720; without 7884 itself that is 12836, so 7884 is abundant (12836 is more than 7884). Euler's totient φ(7884) = 2592 numbers up to 7884 share no factor with it.
- 4
The digits of 7884 add up to 27, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 26 steps to reach 1.
LaTeX source of the formulas on this page
\[ 7884 = 2^{2} \times 3^{3} \times 73 \]7884 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 20720 |
| Euler totient φ(n) | 2592 |
| Square | 62157456 |
| Cube | 490049383104 |
| Square root | 88.791892 (= 6√219) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 26 |
| Scientific notation | 7.884 × |
7884 in other forms
| Form | Value |
|---|---|
| In words | seven thousand eight hundred and eighty-four |
| Binary (base 2) | 1111011001100 |
| Octal (base 8) | 17314 |
| Hexadecimal (base 16) | 1ECC |
| Base 3 | 101211000 |
| As time | 7884 seconds = 2 h 11 min 24 s |
Is 7884 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (7884 ÷ 2 = 3942) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (7884 ÷ 3 = 2628) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (7884 ÷ 4 = 1971) | 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 (7884 ÷ 6 = 1314) | 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 | Yes (7884 ÷ 9 = 876) | 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 8) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (7884 ÷ 12 = 657) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 7884 a prime number?
No. 7884 = × × 73, so it is divisible by 2.
What are the factors of 7884?
1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 73, 108, 146, 219, 292, 438, 657, 876, 1314, 1971, 2628, 3942, 7884.
What is 7884 in binary?
1111011001100 (hexadecimal 1ECC, octal 17314).
What is the square root of 7884?
About 88.7919, exactly 6√219.
Is 7884 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 7884?
7884 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 27.