The number 98072
98072 is a composite number with 32 divisors. Its prime factorisation is × 13 × 23 × 41. Divisors (32): 1, 2, 4, 8, 13, 23, 26, 41, 46, 52, 82, 92, 104, 164, 184, 299 … 98072.
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How to work it out
- 1
What is special about 98072: a Harshad number: divisible by its digit sum 26.
- 2
98072 is composite. Its prime factorisation is
- 3
The divisors add up to 211680; without 98072 itself that is 113608, so 98072 is abundant (113608 is more than 98072). Euler's totient φ(98072) = 42240 numbers up to 98072 share no factor with it.
- 4
The digits of 98072 add up to 26, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 53 steps to reach 1.
LaTeX source of the formulas on this page
\[ 98072 = 2^{3} \times 13 \times 23 \times 41 \]98072 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 211680 |
| Euler totient φ(n) | 42240 |
| Square | 9618117184 |
| Cube | 943267988469248 |
| Square root | 313.164494 (= 2√24518) |
| Digit sum / digital root | 26 / 8 |
| Collatz steps to 1 | 53 |
| Scientific notation | 9.8072 × |
98072 in other forms
| Form | Value |
|---|---|
| In words | ninety-eight thousand and seventy-two |
| Binary (base 2) | 10111111100011000 |
| Octal (base 8) | 277430 |
| Hexadecimal (base 16) | 17F18 |
| Base 3 | 11222112022 |
| As time | 98072 seconds = 27 h 14 min 32 s |
Is 98072 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (98072 ÷ 2 = 49036) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (98072 ÷ 4 = 24518) | 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 | No (remainder 2) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 (98072 ÷ 8 = 12259) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 8) | 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 7) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 98072 a prime number?
No. 98072 = × 13 × 23 × 41, so it is divisible by 2.
What are the factors of 98072?
1, 2, 4, 8, 13, 23, 26, 41, 46, 52, 82, 92, 104, 164, 184, 299, 328, 533, 598, 943, 1066, 1196, 1886, 2132, 2392, 3772, 4264, 7544, 12259, 24518, 49036, 98072.
What is 98072 in binary?
10111111100011000 (hexadecimal 17F18, octal 277430).
What is the square root of 98072?
About 313.1645, exactly 2√24518.
Is 98072 divisible by 3?
No. Its digits add up to 26, which is not a multiple of 3.
What is special about the number 98072?
98072 is a Harshad number: divisible by its digit sum 26.