The number 7740
7740 is a composite number with 36 divisors. Its prime factorisation is × × 5 × 43. Divisors (36): 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 43, 45 … 7740.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 7740: a Harshad number: divisible by its digit sum 18.
- 2
7740 is composite. Its prime factorisation is
- 3
The divisors add up to 24024; without 7740 itself that is 16284, so 7740 is abundant (16284 is more than 7740). Euler's totient φ(7740) = 2016 numbers up to 7740 share no factor with it.
- 4
The digits of 7740 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 145 steps to reach 1.
LaTeX source of the formulas on this page
\[ 7740 = 2^{2} \times 3^{2} \times 5 \times 43 \]7740 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 24024 |
| Euler totient φ(n) | 2016 |
| Square | 59907600 |
| Cube | 463684824000 |
| Square root | 87.977270 (= 6√215) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 145 |
| Scientific notation | 7.74 × |
7740 in other forms
| Form | Value |
|---|---|
| In words | seven thousand seven hundred and forty |
| Binary (base 2) | 1111000111100 |
| Octal (base 8) | 17074 |
| Hexadecimal (base 16) | 1E3C |
| Base 3 | 101121200 |
| As time | 7740 seconds = 2 h 9 min 0 s |
Is 7740 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (7740 ÷ 2 = 3870) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (7740 ÷ 3 = 2580) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (7740 ÷ 4 = 1935) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (7740 ÷ 5 = 1548) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (7740 ÷ 6 = 1290) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 (7740 ÷ 9 = 860) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (7740 ÷ 10 = 774) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 7) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (7740 ÷ 12 = 645) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 7740 a prime number?
No. 7740 = × × 5 × 43, so it is divisible by 2.
What are the factors of 7740?
1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 43, 45, 60, 86, 90, 129, 172, 180, 215, 258, 387, 430, 516, 645, 774, 860, 1290, 1548, 1935, 2580, 3870, 7740.
What is 7740 in binary?
1111000111100 (hexadecimal 1E3C, octal 17074).
What is the square root of 7740?
About 87.9773, exactly 6√215.
Is 7740 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 7740?
7740 is a Harshad number: divisible by its digit sum 18.