The number 780
780 is a triangular number: 1 + 2 + … + 39 = 780. Its prime factorisation is × 3 × 5 × 13. Divisors (24): 1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 20, 26, 30, 39, 52, 60 … 780.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 780: a triangular number: 1 + 2 + … + 39 = 780; a Harshad number: divisible by its digit sum 15.
- 2
780 is composite. Its prime factorisation is
- 3
The divisors add up to 2352; without 780 itself that is 1572, so 780 is abundant (1572 is more than 780). Euler's totient φ(780) = 192 numbers up to 780 share no factor with it.
- 4
The digits of 780 add up to 15, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 121 steps to reach 1.
LaTeX source of the formulas on this page
\[ 780 = 2^{2} \times 3 \times 5 \times 13 \]780 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 2352 |
| Euler totient φ(n) | 192 |
| Square | 608400 |
| Cube | 474552000 |
| Square root | 27.928480 (= 2√195) |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 121 |
| Scientific notation | 7.8 × |
780 in other forms
| Form | Value |
|---|---|
| In words | seven hundred and eighty |
| Roman numerals | DCCLXXX |
| Binary (base 2) | 1100001100 |
| Octal (base 8) | 1414 |
| Hexadecimal (base 16) | 30C |
| Base 3 | 1001220 |
| As time | 780 seconds = 13 min 0 s |
Is 780 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (780 ÷ 2 = 390) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (780 ÷ 3 = 260) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (780 ÷ 4 = 195) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (780 ÷ 5 = 156) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (780 ÷ 6 = 130) | 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 | No (remainder 4) | 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 (780 ÷ 10 = 78) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 10) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (780 ÷ 12 = 65) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 780 a prime number?
No. 780 = × 3 × 5 × 13, so it is divisible by 2.
What are the factors of 780?
1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 20, 26, 30, 39, 52, 60, 65, 78, 130, 156, 195, 260, 390, 780.
What is 780 in binary?
1100001100 (hexadecimal 30C, octal 1414).
What is the square root of 780?
About 27.9285, exactly 2√195.
What is 780 in Roman numerals?
DCCLXXX.
Is 780 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 780?
780 is a triangular number: 1 + 2 + … + 39 = 780; a Harshad number: divisible by its digit sum 15.