The number 98112
98112 is a composite number with 56 divisors. Its prime factorisation is × 3 × 7 × 73. Divisors (56): 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48 … 98112.
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How to work it out
- 1
What is special about 98112: a Harshad number: divisible by its digit sum 21.
- 2
98112 is composite. Its prime factorisation is
- 3
The divisors add up to 300736; without 98112 itself that is 202624, so 98112 is abundant (202624 is more than 98112). Euler's totient φ(98112) = 27648 numbers up to 98112 share no factor with it.
- 4
The digits of 98112 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 53 steps to reach 1.
LaTeX source of the formulas on this page
\[ 98112 = 2^{6} \times 3 \times 7 \times 73 \]98112 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 56 |
| Sum of divisors | 300736 |
| Euler totient φ(n) | 27648 |
| Square | 9625964544 |
| Cube | 944422633340928 |
| Square root | 313.228351 (= 8√1533) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 53 |
| Scientific notation | 9.8112 × |
98112 in other forms
| Form | Value |
|---|---|
| In words | ninety-eight thousand one hundred and twelve |
| Binary (base 2) | 10111111101000000 |
| Octal (base 8) | 277500 |
| Hexadecimal (base 16) | 17F40 |
| Base 3 | 11222120210 |
| As time | 98112 seconds = 27 h 15 min 12 s |
Is 98112 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (98112 ÷ 2 = 49056) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (98112 ÷ 3 = 32704) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (98112 ÷ 4 = 24528) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 2) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (98112 ÷ 6 = 16352) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (98112 ÷ 7 = 14016) | 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 (98112 ÷ 8 = 12264) | 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 2) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 3) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (98112 ÷ 12 = 8176) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 98112 a prime number?
No. 98112 = × 3 × 7 × 73, so it is divisible by 2.
What are the factors of 98112?
1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48, 56, 64, 73, 84, 96, 112, 146, 168, 192, 219, 224, 292, 336, 438, 448, 511, 584, 672, 876, 1022, 1168, 1344, 1533, 1752, 2044, 2336, 3066, 3504, 4088, 4672, 6132, 7008, 8176, 12264, 14016, 16352, 24528, 32704, 49056, 98112.
What is 98112 in binary?
10111111101000000 (hexadecimal 17F40, octal 277500).
What is the square root of 98112?
About 313.2284, exactly 8√1533.
Is 98112 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 98112?
98112 is a Harshad number: divisible by its digit sum 21.