The number 784
784 is a perfect square (28²). Its prime factorisation is × . Divisors (15): 1, 2, 4, 7, 8, 14, 16, 28, 49, 56, 98, 112, 196, 392, 784.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 784: a perfect square (28²); a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
784 is composite. Its prime factorisation is
- 3
The divisors add up to 1767; without 784 itself that is 983, so 784 is abundant (983 is more than 784). Euler's totient φ(784) = 336 numbers up to 784 share no factor with it.
- 4
The digits of 784 add up to 19, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 28 steps to reach 1.
LaTeX source of the formulas on this page
\[ 784 = 2^{4} \times 7^{2} \]784 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 15 |
| Sum of divisors | 1767 |
| Euler totient φ(n) | 336 |
| Square | 614656 |
| Cube | 481890304 |
| Square root | 28 |
| Digit sum / digital root | 19 / 1 |
| Collatz steps to 1 | 28 |
| Scientific notation | 7.84 × |
| Perfect power |
784 in other forms
| Form | Value |
|---|---|
| In words | seven hundred and eighty-four |
| Roman numerals | DCCLXXXIV |
| Binary (base 2) | 1100010000 |
| Octal (base 8) | 1420 |
| Hexadecimal (base 16) | 310 |
| Base 3 | 1002001 |
| As time | 784 seconds = 13 min 4 s |
Is 784 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (784 ÷ 2 = 392) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (784 ÷ 4 = 196) | 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 | No (remainder 4) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (784 ÷ 7 = 112) | 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 (784 ÷ 8 = 98) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 1) | 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 3) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 784 a prime number?
No. 784 = × , so it is divisible by 2.
What are the factors of 784?
1, 2, 4, 7, 8, 14, 16, 28, 49, 56, 98, 112, 196, 392, 784.
What is 784 in binary?
1100010000 (hexadecimal 310, octal 1420).
What is the square root of 784?
28, because 28 × 28 = 784.
What is 784 in Roman numerals?
DCCLXXXIV.
Is 784 divisible by 3?
No. Its digits add up to 19, which is not a multiple of 3.
What is special about the number 784?
784 is a perfect square (28²); a happy number: repeatedly adding the squares of its digits reaches 1.