The number 83124
83124 is a composite number with 18 divisors. Its prime factorisation is × × 2309. Divisors (18): 1, 2, 3, 4, 6, 9, 12, 18, 36, 2309, 4618, 6927, 9236, 13854, 20781, 27708 … 83124.
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How to work it out
- 1
What is special about 83124: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.
- 2
83124 is composite. Its prime factorisation is
- 3
The divisors add up to 210210; without 83124 itself that is 127086, so 83124 is abundant (127086 is more than 83124). Euler's totient φ(83124) = 27696 numbers up to 83124 share no factor with it.
- 4
The digits of 83124 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 107 steps to reach 1.
LaTeX source of the formulas on this page
\[ 83124 = 2^{2} \times 3^{2} \times 2309 \]83124 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 18 |
| Sum of divisors | 210210 |
| Euler totient φ(n) | 27696 |
| Square | 6909599376 |
| Cube | 574353538530624 |
| Square root | 288.312331 (= 6√2309) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 107 |
| Scientific notation | 8.3124 × |
83124 in other forms
| Form | Value |
|---|---|
| In words | eighty-three thousand one hundred and twenty-four |
| Binary (base 2) | 10100010010110100 |
| Octal (base 8) | 242264 |
| Hexadecimal (base 16) | 144B4 |
| Base 3 | 11020000200 |
| As time | 83124 seconds = 23 h 5 min 24 s |
Is 83124 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (83124 ÷ 2 = 41562) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (83124 ÷ 3 = 27708) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (83124 ÷ 4 = 20781) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 4) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (83124 ÷ 6 = 13854) | 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 | No (remainder 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (83124 ÷ 9 = 9236) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 4) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 8) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (83124 ÷ 12 = 6927) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 83124 a prime number?
No. 83124 = × × 2309, so it is divisible by 2.
What are the factors of 83124?
1, 2, 3, 4, 6, 9, 12, 18, 36, 2309, 4618, 6927, 9236, 13854, 20781, 27708, 41562, 83124.
What is 83124 in binary?
10100010010110100 (hexadecimal 144B4, octal 242264).
What is the square root of 83124?
About 288.3123, exactly 6√2309.
Is 83124 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 83124?
83124 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.