The number 7920
7920 is a composite number with 60 divisors. Its prime factorisation is × × 5 × 11. Divisors (60): 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 15, 16, 18, 20, 22 … 7920.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 7920: a Harshad number: divisible by its digit sum 18.
- 2
7920 is composite. Its prime factorisation is
- 3
The divisors add up to 29016; without 7920 itself that is 21096, so 7920 is abundant (21096 is more than 7920). Euler's totient φ(7920) = 1920 numbers up to 7920 share no factor with it.
- 4
The digits of 7920 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 101 steps to reach 1.
LaTeX source of the formulas on this page
\[ 7920 = 2^{4} \times 3^{2} \times 5 \times 11 \]7920 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 60 |
| Sum of divisors | 29016 |
| Euler totient φ(n) | 1920 |
| Square | 62726400 |
| Cube | 496793088000 |
| Square root | 88.994382 (= 12√55) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 101 |
| Scientific notation | 7.92 × |
7920 in other forms
| Form | Value |
|---|---|
| In words | seven thousand nine hundred and twenty |
| Binary (base 2) | 1111011110000 |
| Octal (base 8) | 17360 |
| Hexadecimal (base 16) | 1EF0 |
| Base 3 | 101212100 |
| As time | 7920 seconds = 2 h 12 min 0 s |
Is 7920 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (7920 ÷ 2 = 3960) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (7920 ÷ 3 = 2640) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (7920 ÷ 4 = 1980) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (7920 ÷ 5 = 1584) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (7920 ÷ 6 = 1320) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 (7920 ÷ 8 = 990) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (7920 ÷ 9 = 880) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (7920 ÷ 10 = 792) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (7920 ÷ 11 = 720) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (7920 ÷ 12 = 660) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 7920 a prime number?
No. 7920 = × × 5 × 11, so it is divisible by 2.
What are the factors of 7920?
1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 15, 16, 18, 20, 22, 24, 30, 33, 36, 40, 44, 45, 48, 55, 60, 66, 72, 80, 88, 90, 99, 110, 120, 132, 144, 165, 176, 180, 198, 220, 240, 264, 330, 360, 396, 440, 495, 528, 660, 720, 792, 880, 990, 1320, 1584, 1980, 2640, 3960, 7920.
What is 7920 in binary?
1111011110000 (hexadecimal 1EF0, octal 17360).
What is the square root of 7920?
About 88.9944, exactly 12√55.
Is 7920 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 7920?
7920 is a Harshad number: divisible by its digit sum 18.