The number 73776
73776 is a composite number with 40 divisors. Its prime factorisation is × 3 × 29 × 53. Divisors (40): 1, 2, 3, 4, 6, 8, 12, 16, 24, 29, 48, 53, 58, 87, 106, 116 … 73776.
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How to work it out
- 1
What is special about 73776: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
73776 is composite. Its prime factorisation is
- 3
The divisors add up to 200880; without 73776 itself that is 127104, so 73776 is abundant (127104 is more than 73776). Euler's totient φ(73776) = 23296 numbers up to 73776 share no factor with it.
- 4
The digits of 73776 add up to 30, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 112 steps to reach 1.
LaTeX source of the formulas on this page
\[ 73776 = 2^{4} \times 3 \times 29 \times 53 \]73776 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 40 |
| Sum of divisors | 200880 |
| Euler totient φ(n) | 23296 |
| Square | 5442898176 |
| Cube | 401555255832576 |
| Square root | 271.617378 (= 4√4611) |
| Digit sum / digital root | 30 / 3 |
| Collatz steps to 1 | 112 |
| Scientific notation | 7.3776 × |
73776 in other forms
| Form | Value |
|---|---|
| In words | seventy-three thousand seven hundred and seventy-six |
| Binary (base 2) | 10010000000110000 |
| Octal (base 8) | 220060 |
| Hexadecimal (base 16) | 12030 |
| Base 3 | 10202012110 |
| As time | 73776 seconds = 20 h 29 min 36 s |
Is 73776 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (73776 ÷ 2 = 36888) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (73776 ÷ 3 = 24592) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (73776 ÷ 4 = 18444) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 1) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (73776 ÷ 6 = 12296) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 (73776 ÷ 8 = 9222) | 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 6) | 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 (73776 ÷ 12 = 6148) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 73776 a prime number?
No. 73776 = × 3 × 29 × 53, so it is divisible by 2.
What are the factors of 73776?
1, 2, 3, 4, 6, 8, 12, 16, 24, 29, 48, 53, 58, 87, 106, 116, 159, 174, 212, 232, 318, 348, 424, 464, 636, 696, 848, 1272, 1392, 1537, 2544, 3074, 4611, 6148, 9222, 12296, 18444, 24592, 36888, 73776.
What is 73776 in binary?
10010000000110000 (hexadecimal 12030, octal 220060).
What is the square root of 73776?
About 271.6174, exactly 4√4611.
Is 73776 divisible by 3?
Yes. Its digits add up to 30, a multiple of 3.
What is special about the number 73776?
73776 is a happy number: repeatedly adding the squares of its digits reaches 1.