The number 73968
73968 is a composite number with 40 divisors. Its prime factorisation is × 3 × 23 × 67. Divisors (40): 1, 2, 3, 4, 6, 8, 12, 16, 23, 24, 46, 48, 67, 69, 92, 134 … 73968.
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How to work it out
- 1
What is special about 73968: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
73968 is composite. Its prime factorisation is
- 3
The divisors add up to 202368; without 73968 itself that is 128400, so 73968 is abundant (128400 is more than 73968). Euler's totient φ(73968) = 23232 numbers up to 73968 share no factor with it.
- 4
The digits of 73968 add up to 33, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 156 steps to reach 1.
LaTeX source of the formulas on this page
\[ 73968 = 2^{4} \times 3 \times 23 \times 67 \]73968 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 40 |
| Sum of divisors | 202368 |
| Euler totient φ(n) | 23232 |
| Square | 5471265024 |
| Cube | 404698531295232 |
| Square root | 271.970587 (= 4√4623) |
| Digit sum / digital root | 33 / 6 |
| Collatz steps to 1 | 156 |
| Scientific notation | 7.3968 × |
73968 in other forms
| Form | Value |
|---|---|
| In words | seventy-three thousand nine hundred and sixty-eight |
| Binary (base 2) | 10010000011110000 |
| Octal (base 8) | 220360 |
| Hexadecimal (base 16) | 120F0 |
| Base 3 | 10202110120 |
| As time | 73968 seconds = 20 h 32 min 48 s |
Is 73968 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (73968 ÷ 2 = 36984) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (73968 ÷ 3 = 24656) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (73968 ÷ 4 = 18492) | 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 (73968 ÷ 6 = 12328) | 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 (73968 ÷ 8 = 9246) | 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 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (73968 ÷ 12 = 6164) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 73968 a prime number?
No. 73968 = × 3 × 23 × 67, so it is divisible by 2.
What are the factors of 73968?
1, 2, 3, 4, 6, 8, 12, 16, 23, 24, 46, 48, 67, 69, 92, 134, 138, 184, 201, 268, 276, 368, 402, 536, 552, 804, 1072, 1104, 1541, 1608, 3082, 3216, 4623, 6164, 9246, 12328, 18492, 24656, 36984, 73968.
What is 73968 in binary?
10010000011110000 (hexadecimal 120F0, octal 220360).
What is the square root of 73968?
About 271.9706, exactly 4√4623.
Is 73968 divisible by 3?
Yes. Its digits add up to 33, a multiple of 3.
What is special about the number 73968?
73968 is a happy number: repeatedly adding the squares of its digits reaches 1.