The number 7744
7744 is a perfect square (88²). Its prime factorisation is × . Divisors (21): 1, 2, 4, 8, 11, 16, 22, 32, 44, 64, 88, 121, 176, 242, 352, 484 … 7744.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 7744: a perfect square (88²); a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 22.
- 2
7744 is composite. Its prime factorisation is
- 3
The divisors add up to 16891; without 7744 itself that is 9147, so 7744 is abundant (9147 is more than 7744). Euler's totient φ(7744) = 3520 numbers up to 7744 share no factor with it.
- 4
The digits of 7744 add up to 22, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 101 steps to reach 1.
LaTeX source of the formulas on this page
\[ 7744 = 2^{6} \times 11^{2} \]7744 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 21 |
| Sum of divisors | 16891 |
| Euler totient φ(n) | 3520 |
| Square | 59969536 |
| Cube | 464404086784 |
| Square root | 88 |
| Digit sum / digital root | 22 / 4 |
| Collatz steps to 1 | 101 |
| Scientific notation | 7.744 × |
| Perfect power |
7744 in other forms
| Form | Value |
|---|---|
| In words | seven thousand seven hundred and forty-four |
| Binary (base 2) | 1111001000000 |
| Octal (base 8) | 17100 |
| Hexadecimal (base 16) | 1E40 |
| Base 3 | 101121211 |
| As time | 7744 seconds = 2 h 9 min 4 s |
Is 7744 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (7744 ÷ 2 = 3872) | 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 (7744 ÷ 4 = 1936) | 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 | 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 | Yes (7744 ÷ 8 = 968) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 4) | 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 | Yes (7744 ÷ 11 = 704) | 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 7744 a prime number?
No. 7744 = × , so it is divisible by 2.
What are the factors of 7744?
1, 2, 4, 8, 11, 16, 22, 32, 44, 64, 88, 121, 176, 242, 352, 484, 704, 968, 1936, 3872, 7744.
What is 7744 in binary?
1111001000000 (hexadecimal 1E40, octal 17100).
What is the square root of 7744?
88, because 88 × 88 = 7744.
Is 7744 divisible by 3?
No. Its digits add up to 22, which is not a multiple of 3.
What is special about the number 7744?
7744 is a perfect square (88²); a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 22.