The number 73248
73248 is a composite number with 48 divisors. Its prime factorisation is × 3 × 7 × 109. Divisors (48): 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48 … 73248.
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How to work it out
- 1
What is special about 73248: a Harshad number: divisible by its digit sum 24.
- 2
73248 is composite. Its prime factorisation is
- 3
The divisors add up to 221760; without 73248 itself that is 148512, so 73248 is abundant (148512 is more than 73248). Euler's totient φ(73248) = 20736 numbers up to 73248 share no factor with it.
- 4
The digits of 73248 add up to 24, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 112 steps to reach 1.
LaTeX source of the formulas on this page
\[ 73248 = 2^{5} \times 3 \times 7 \times 109 \]73248 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 221760 |
| Euler totient φ(n) | 20736 |
| Square | 5365269504 |
| Cube | 392995260628992 |
| Square root | 270.643677 (= 4√4578) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 112 |
| Scientific notation | 7.3248 × |
73248 in other forms
| Form | Value |
|---|---|
| In words | seventy-three thousand two hundred and forty-eight |
| Binary (base 2) | 10001111000100000 |
| Octal (base 8) | 217040 |
| Hexadecimal (base 16) | 11E20 |
| Base 3 | 10201110220 |
| As time | 73248 seconds = 20 h 20 min 48 s |
Is 73248 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (73248 ÷ 2 = 36624) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (73248 ÷ 3 = 24416) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (73248 ÷ 4 = 18312) | 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 (73248 ÷ 6 = 12208) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (73248 ÷ 7 = 10464) | 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 (73248 ÷ 8 = 9156) | 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 | No (remainder 8) | 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 (73248 ÷ 12 = 6104) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 73248 a prime number?
No. 73248 = × 3 × 7 × 109, so it is divisible by 2.
What are the factors of 73248?
1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48, 56, 84, 96, 109, 112, 168, 218, 224, 327, 336, 436, 654, 672, 763, 872, 1308, 1526, 1744, 2289, 2616, 3052, 3488, 4578, 5232, 6104, 9156, 10464, 12208, 18312, 24416, 36624, 73248.
What is 73248 in binary?
10001111000100000 (hexadecimal 11E20, octal 217040).
What is the square root of 73248?
About 270.6437, exactly 4√4578.
Is 73248 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 73248?
73248 is a Harshad number: divisible by its digit sum 24.