The number 72480
72480 is a composite number with 48 divisors. Its prime factorisation is × 3 × 5 × 151. Divisors (48): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40 … 72480.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 72480: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
72480 is composite. Its prime factorisation is
- 3
The divisors add up to 229824; without 72480 itself that is 157344, so 72480 is abundant (157344 is more than 72480). Euler's totient φ(72480) = 19200 numbers up to 72480 share no factor with it.
- 4
The digits of 72480 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 68 steps to reach 1.
LaTeX source of the formulas on this page
\[ 72480 = 2^{5} \times 3 \times 5 \times 151 \]72480 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 229824 |
| Euler totient φ(n) | 19200 |
| Square | 5253350400 |
| Cube | 380762836992000 |
| Square root | 269.221099 (= 4√4530) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 68 |
| Scientific notation | 7.248 × |
72480 in other forms
| Form | Value |
|---|---|
| In words | seventy-two thousand four hundred and eighty |
| Binary (base 2) | 10001101100100000 |
| Octal (base 8) | 215440 |
| Hexadecimal (base 16) | 11B20 |
| Base 3 | 10200102110 |
| As time | 72480 seconds = 20 h 8 min 0 s |
Is 72480 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (72480 ÷ 2 = 36240) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (72480 ÷ 3 = 24160) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (72480 ÷ 4 = 18120) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (72480 ÷ 5 = 14496) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (72480 ÷ 6 = 12080) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 (72480 ÷ 8 = 9060) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (72480 ÷ 10 = 7248) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (72480 ÷ 12 = 6040) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 72480 a prime number?
No. 72480 = × 3 × 5 × 151, so it is divisible by 2.
What are the factors of 72480?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 80, 96, 120, 151, 160, 240, 302, 453, 480, 604, 755, 906, 1208, 1510, 1812, 2265, 2416, 3020, 3624, 4530, 4832, 6040, 7248, 9060, 12080, 14496, 18120, 24160, 36240, 72480.
What is 72480 in binary?
10001101100100000 (hexadecimal 11B20, octal 215440).
What is the square root of 72480?
About 269.2211, exactly 4√4530.
Is 72480 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 72480?
72480 is a happy number: repeatedly adding the squares of its digits reaches 1.