The number 72840
72840 is a composite number with 32 divisors. Its prime factorisation is × 3 × 5 × 607. Divisors (32): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120 … 72840.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 72840: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
72840 is composite. Its prime factorisation is
- 3
The divisors add up to 218880; without 72840 itself that is 146040, so 72840 is abundant (146040 is more than 72840). Euler's totient φ(72840) = 19392 numbers up to 72840 share no factor with it.
- 4
The digits of 72840 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 156 steps to reach 1.
LaTeX source of the formulas on this page
\[ 72840 = 2^{3} \times 3 \times 5 \times 607 \]72840 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 218880 |
| Euler totient φ(n) | 19392 |
| Square | 5305665600 |
| Cube | 386464682304000 |
| Square root | 269.888866 (= 2√18210) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 156 |
| Scientific notation | 7.284 × |
72840 in other forms
| Form | Value |
|---|---|
| In words | seventy-two thousand eight hundred and forty |
| Binary (base 2) | 10001110010001000 |
| Octal (base 8) | 216210 |
| Hexadecimal (base 16) | 11C88 |
| Base 3 | 10200220210 |
| As time | 72840 seconds = 20 h 14 min 0 s |
Is 72840 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (72840 ÷ 2 = 36420) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (72840 ÷ 3 = 24280) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (72840 ÷ 4 = 18210) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (72840 ÷ 5 = 14568) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (72840 ÷ 6 = 12140) | 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 (72840 ÷ 8 = 9105) | 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 (72840 ÷ 10 = 7284) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 9) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (72840 ÷ 12 = 6070) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 72840 a prime number?
No. 72840 = × 3 × 5 × 607, so it is divisible by 2.
What are the factors of 72840?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120, 607, 1214, 1821, 2428, 3035, 3642, 4856, 6070, 7284, 9105, 12140, 14568, 18210, 24280, 36420, 72840.
What is 72840 in binary?
10001110010001000 (hexadecimal 11C88, octal 216210).
What is the square root of 72840?
About 269.8889, exactly 2√18210.
Is 72840 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 72840?
72840 is a happy number: repeatedly adding the squares of its digits reaches 1.