The number 83976
83976 is a composite number with 16 divisors. Its prime factorisation is × 3 × 3499. Divisors (16): 1, 2, 3, 4, 6, 8, 12, 24, 3499, 6998, 10497, 13996, 20994, 27992, 41988, 83976.
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How to work it out
- 1
What is special about 83976: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
83976 is composite. Its prime factorisation is
- 3
The divisors add up to 210000; without 83976 itself that is 126024, so 83976 is abundant (126024 is more than 83976). Euler's totient φ(83976) = 27984 numbers up to 83976 share no factor with it.
- 4
The digits of 83976 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 151 steps to reach 1.
LaTeX source of the formulas on this page
\[ 83976 = 2^{3} \times 3 \times 3499 \]83976 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 210000 |
| Euler totient φ(n) | 27984 |
| Square | 7051968576 |
| Cube | 592196113138176 |
| Square root | 289.786128 (= 2√20994) |
| Digit sum / digital root | 33 / 6 |
| Collatz steps to 1 | 151 |
| Scientific notation | 8.3976 × |
83976 in other forms
| Form | Value |
|---|---|
| In words | eighty-three thousand nine hundred and seventy-six |
| Binary (base 2) | 10100100000001000 |
| Octal (base 8) | 244010 |
| Hexadecimal (base 16) | 14808 |
| Base 3 | 11021012020 |
| As time | 83976 seconds = 23 h 19 min 36 s |
Is 83976 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (83976 ÷ 2 = 41988) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (83976 ÷ 3 = 27992) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (83976 ÷ 4 = 20994) | 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 (83976 ÷ 6 = 13996) | 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 (83976 ÷ 8 = 10497) | 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 6) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 2) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (83976 ÷ 12 = 6998) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 83976 a prime number?
No. 83976 = × 3 × 3499, so it is divisible by 2.
What are the factors of 83976?
1, 2, 3, 4, 6, 8, 12, 24, 3499, 6998, 10497, 13996, 20994, 27992, 41988, 83976.
What is 83976 in binary?
10100100000001000 (hexadecimal 14808, octal 244010).
What is the square root of 83976?
About 289.7861, exactly 2√20994.
Is 83976 divisible by 3?
Yes. Its digits add up to 33, a multiple of 3.
What is special about the number 83976?
83976 is a happy number: repeatedly adding the squares of its digits reaches 1.