The number 80976
80976 is a composite number with 40 divisors. Its prime factorisation is × 3 × 7 × 241. Divisors (40): 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 56 … 80976.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 80976: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
80976 is composite. Its prime factorisation is
- 3
The divisors add up to 240064; without 80976 itself that is 159088, so 80976 is abundant (159088 is more than 80976). Euler's totient φ(80976) = 23040 numbers up to 80976 share no factor with it.
- 4
The digits of 80976 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 45 steps to reach 1.
LaTeX source of the formulas on this page
\[ 80976 = 2^{4} \times 3 \times 7 \times 241 \]80976 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 40 |
| Sum of divisors | 240064 |
| Euler totient φ(n) | 23040 |
| Square | 6557112576 |
| Cube | 530968747954176 |
| Square root | 284.562823 (= 4√5061) |
| Digit sum / digital root | 30 / 3 |
| Collatz steps to 1 | 45 |
| Scientific notation | 8.0976 × |
80976 in other forms
| Form | Value |
|---|---|
| In words | eighty thousand nine hundred and seventy-six |
| Binary (base 2) | 10011110001010000 |
| Octal (base 8) | 236120 |
| Hexadecimal (base 16) | 13C50 |
| Base 3 | 11010002010 |
| As time | 80976 seconds = 22 h 29 min 36 s |
Is 80976 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (80976 ÷ 2 = 40488) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (80976 ÷ 3 = 26992) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (80976 ÷ 4 = 20244) | 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 (80976 ÷ 6 = 13496) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (80976 ÷ 7 = 11568) | 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 (80976 ÷ 8 = 10122) | 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 5) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (80976 ÷ 12 = 6748) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 80976 a prime number?
No. 80976 = × 3 × 7 × 241, so it is divisible by 2.
What are the factors of 80976?
1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 56, 84, 112, 168, 241, 336, 482, 723, 964, 1446, 1687, 1928, 2892, 3374, 3856, 5061, 5784, 6748, 10122, 11568, 13496, 20244, 26992, 40488, 80976.
What is 80976 in binary?
10011110001010000 (hexadecimal 13C50, octal 236120).
What is the square root of 80976?
About 284.5628, exactly 4√5061.
Is 80976 divisible by 3?
Yes. Its digits add up to 30, a multiple of 3.
What is special about the number 80976?
80976 is a happy number: repeatedly adding the squares of its digits reaches 1.