The number 88100
88100 is a composite number with 18 divisors. Its prime factorisation is × × 881. Divisors (18): 1, 2, 4, 5, 10, 20, 25, 50, 100, 881, 1762, 3524, 4405, 8810, 17620, 22025 … 88100.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 88100: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
88100 is composite. Its prime factorisation is
- 3
The divisors add up to 191394; without 88100 itself that is 103294, so 88100 is abundant (103294 is more than 88100). Euler's totient φ(88100) = 35200 numbers up to 88100 share no factor with it.
- 4
The digits of 88100 add up to 17, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 71 steps to reach 1.
LaTeX source of the formulas on this page
\[ 88100 = 2^{2} \times 5^{2} \times 881 \]88100 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 18 |
| Sum of divisors | 191394 |
| Euler totient φ(n) | 35200 |
| Square | 7761610000 |
| Cube | 683797841000000 |
| Square root | 296.816442 (= 10√881) |
| Digit sum / digital root | 17 / 8 |
| Collatz steps to 1 | 71 |
| Scientific notation | 8.81 × |
88100 in other forms
| Form | Value |
|---|---|
| In words | eighty-eight thousand one hundred |
| Binary (base 2) | 10101100000100100 |
| Octal (base 8) | 254044 |
| Hexadecimal (base 16) | 15824 |
| Base 3 | 11110211222 |
| As time | 88100 seconds = 24 h 28 min 20 s |
Is 88100 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (88100 ÷ 2 = 44050) | 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 (88100 ÷ 4 = 22025) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (88100 ÷ 5 = 17620) | 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 5) | 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 | No (remainder 8) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (88100 ÷ 10 = 8810) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 1) | 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 88100 a prime number?
No. 88100 = × × 881, so it is divisible by 2.
What are the factors of 88100?
1, 2, 4, 5, 10, 20, 25, 50, 100, 881, 1762, 3524, 4405, 8810, 17620, 22025, 44050, 88100.
What is 88100 in binary?
10101100000100100 (hexadecimal 15824, octal 254044).
What is the square root of 88100?
About 296.8164, exactly 10√881.
Is 88100 divisible by 3?
No. Its digits add up to 17, which is not a multiple of 3.
What is special about the number 88100?
88100 is a happy number: repeatedly adding the squares of its digits reaches 1.