The number 78720
78720 is a composite number with 64 divisors. Its prime factorisation is × 3 × 5 × 41. Divisors (64): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40 … 78720.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 78720: a Harshad number: divisible by its digit sum 24.
- 2
78720 is composite. Its prime factorisation is
- 3
The divisors add up to 257040; without 78720 itself that is 178320, so 78720 is abundant (178320 is more than 78720). Euler's totient φ(78720) = 20480 numbers up to 78720 share no factor with it.
- 4
The digits of 78720 add up to 24, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 76 steps to reach 1.
LaTeX source of the formulas on this page
\[ 78720 = 2^{7} \times 3 \times 5 \times 41 \]78720 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 64 |
| Sum of divisors | 257040 |
| Euler totient φ(n) | 20480 |
| Square | 6196838400 |
| Cube | 487815118848000 |
| Square root | 280.570847 (= 8√1230) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 76 |
| Scientific notation | 7.872 × |
78720 in other forms
| Form | Value |
|---|---|
| In words | seventy-eight thousand seven hundred and twenty |
| Binary (base 2) | 10011001110000000 |
| Octal (base 8) | 231600 |
| Hexadecimal (base 16) | 13380 |
| Base 3 | 10222222120 |
| As time | 78720 seconds = 21 h 52 min 0 s |
Is 78720 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (78720 ÷ 2 = 39360) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (78720 ÷ 3 = 26240) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (78720 ÷ 4 = 19680) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (78720 ÷ 5 = 15744) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (78720 ÷ 6 = 13120) | 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 | Yes (78720 ÷ 8 = 9840) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (78720 ÷ 10 = 7872) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (78720 ÷ 12 = 6560) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 78720 a prime number?
No. 78720 = × 3 × 5 × 41, so it is divisible by 2.
What are the factors of 78720?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 41, 48, 60, 64, 80, 82, 96, 120, 123, 128, 160, 164, 192, 205, 240, 246, 320, 328, 384, 410, 480, 492, 615, 640, 656, 820, 960, 984, 1230, 1312, 1640, 1920, 1968, 2460, 2624, 3280, 3936, 4920, 5248, 6560, 7872, 9840, 13120, 15744, 19680, 26240, 39360, 78720.
What is 78720 in binary?
10011001110000000 (hexadecimal 13380, octal 231600).
What is the square root of 78720?
About 280.5708, exactly 8√1230.
Is 78720 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 78720?
78720 is a Harshad number: divisible by its digit sum 24.