The number 720
720 is a highly composite number: it has 30 divisors, more than any smaller number and 6! (6 factorial). Its prime factorisation is × × 5. Divisors (30): 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30 … 720.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 720: a highly composite number: it has 30 divisors, more than any smaller number; 6! (6 factorial); a Harshad number: divisible by its digit sum 9.
- 2
720 is composite. Its prime factorisation is
- 3
The divisors add up to 2418; without 720 itself that is 1698, so 720 is abundant (1698 is more than 720). Euler's totient φ(720) = 192 numbers up to 720 share no factor with it.
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The digits of 720 add up to 9, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 20 steps to reach 1.
LaTeX source of the formulas on this page
\[ 720 = 2^{4} \times 3^{2} \times 5 \]720 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 30 |
| Sum of divisors | 2418 |
| Euler totient φ(n) | 192 |
| Square | 518400 |
| Cube | 373248000 |
| Square root | 26.832816 (= 12√5) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 20 |
| Scientific notation | 7.2 × |
720 in other forms
| Form | Value |
|---|---|
| In words | seven hundred and twenty |
| Roman numerals | DCCXX |
| Binary (base 2) | 1011010000 |
| Octal (base 8) | 1320 |
| Hexadecimal (base 16) | 2D0 |
| Base 3 | 222200 |
| As time | 720 seconds = 12 min 0 s |
Is 720 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (720 ÷ 2 = 360) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (720 ÷ 3 = 240) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (720 ÷ 4 = 180) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (720 ÷ 5 = 144) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (720 ÷ 6 = 120) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | 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 (720 ÷ 8 = 90) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (720 ÷ 9 = 80) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (720 ÷ 10 = 72) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 5) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (720 ÷ 12 = 60) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 720 a prime number?
No. 720 = × × 5, so it is divisible by 2.
What are the factors of 720?
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 48, 60, 72, 80, 90, 120, 144, 180, 240, 360, 720.
What is 720 in binary?
1011010000 (hexadecimal 2D0, octal 1320).
What is the square root of 720?
About 26.8328, exactly 12√5.
What is 720 in Roman numerals?
DCCXX.
Is 720 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 720?
720 is a highly composite number: it has 30 divisors, more than any smaller number; 6! (6 factorial); a Harshad number: divisible by its digit sum 9.