The number 98100
98100 is a composite number with 54 divisors. Its prime factorisation is × × × 109. Divisors (54): 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45 … 98100.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 98100: a Harshad number: divisible by its digit sum 18.
- 2
98100 is composite. Its prime factorisation is
- 3
The divisors add up to 310310; without 98100 itself that is 212210, so 98100 is abundant (212210 is more than 98100). Euler's totient φ(98100) = 25920 numbers up to 98100 share no factor with it.
- 4
The digits of 98100 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 159 steps to reach 1.
LaTeX source of the formulas on this page
\[ 98100 = 2^{2} \times 3^{2} \times 5^{2} \times 109 \]98100 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 54 |
| Sum of divisors | 310310 |
| Euler totient φ(n) | 25920 |
| Square | 9623610000 |
| Cube | 944076141000000 |
| Square root | 313.209195 (= 30√109) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 159 |
| Scientific notation | 9.81 × |
98100 in other forms
| Form | Value |
|---|---|
| In words | ninety-eight thousand one hundred |
| Binary (base 2) | 10111111100110100 |
| Octal (base 8) | 277464 |
| Hexadecimal (base 16) | 17F34 |
| Base 3 | 11222120100 |
| As time | 98100 seconds = 27 h 15 min 0 s |
Is 98100 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (98100 ÷ 2 = 49050) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (98100 ÷ 3 = 32700) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (98100 ÷ 4 = 24525) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (98100 ÷ 5 = 19620) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (98100 ÷ 6 = 16350) | 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 | No (remainder 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (98100 ÷ 9 = 10900) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (98100 ÷ 10 = 9810) | 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 (98100 ÷ 12 = 8175) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 98100 a prime number?
No. 98100 = × × × 109, so it is divisible by 2.
What are the factors of 98100?
1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 109, 150, 180, 218, 225, 300, 327, 436, 450, 545, 654, 900, 981, 1090, 1308, 1635, 1962, 2180, 2725, 3270, 3924, 4905, 5450, 6540, 8175, 9810, 10900, 16350, 19620, 24525, 32700, 49050, 98100.
What is 98100 in binary?
10111111100110100 (hexadecimal 17F34, octal 277464).
What is the square root of 98100?
About 313.2092, exactly 30√109.
Is 98100 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 98100?
98100 is a Harshad number: divisible by its digit sum 18.