The number 72048
72048 is a composite number with 40 divisors. Its prime factorisation is × 3 × 19 × 79. Divisors (40): 1, 2, 3, 4, 6, 8, 12, 16, 19, 24, 38, 48, 57, 76, 79, 114 … 72048.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 72048: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
72048 is composite. Its prime factorisation is
- 3
The divisors add up to 198400; without 72048 itself that is 126352, so 72048 is abundant (126352 is more than 72048). Euler's totient φ(72048) = 22464 numbers up to 72048 share no factor with it.
- 4
The digits of 72048 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 42 steps to reach 1.
LaTeX source of the formulas on this page
\[ 72048 = 2^{4} \times 3 \times 19 \times 79 \]72048 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 40 |
| Sum of divisors | 198400 |
| Euler totient φ(n) | 22464 |
| Square | 5190914304 |
| Cube | 373994993774592 |
| Square root | 268.417585 (= 4√4503) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 42 |
| Scientific notation | 7.2048 × |
72048 in other forms
| Form | Value |
|---|---|
| In words | seventy-two thousand and forty-eight |
| Binary (base 2) | 10001100101110000 |
| Octal (base 8) | 214560 |
| Hexadecimal (base 16) | 11970 |
| Base 3 | 10122211110 |
| As time | 72048 seconds = 20 h 0 min 48 s |
Is 72048 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (72048 ÷ 2 = 36024) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (72048 ÷ 3 = 24016) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (72048 ÷ 4 = 18012) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 3) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (72048 ÷ 6 = 12008) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 (72048 ÷ 8 = 9006) | 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 | No (remainder 8) | 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 (72048 ÷ 12 = 6004) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 72048 a prime number?
No. 72048 = × 3 × 19 × 79, so it is divisible by 2.
What are the factors of 72048?
1, 2, 3, 4, 6, 8, 12, 16, 19, 24, 38, 48, 57, 76, 79, 114, 152, 158, 228, 237, 304, 316, 456, 474, 632, 912, 948, 1264, 1501, 1896, 3002, 3792, 4503, 6004, 9006, 12008, 18012, 24016, 36024, 72048.
What is 72048 in binary?
10001100101110000 (hexadecimal 11970, octal 214560).
What is the square root of 72048?
About 268.4176, exactly 4√4503.
Is 72048 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 72048?
72048 is a happy number: repeatedly adding the squares of its digits reaches 1.