The number 88102
88102 is a composite number with 24 divisors. Its prime factorisation is 2 × × 29 × 31. Divisors (24): 1, 2, 7, 14, 29, 31, 49, 58, 62, 98, 203, 217, 406, 434, 899, 1421 … 88102.
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How to work it out
- 1
What is special about 88102: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
88102 is composite. Its prime factorisation is
- 3
The divisors add up to 164160; without 88102 itself that is 76058, so 88102 is deficient (76058 is less than 88102). Euler's totient φ(88102) = 35280 numbers up to 88102 share no factor with it.
- 4
The digits of 88102 add up to 19, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 71 steps to reach 1.
LaTeX source of the formulas on this page
\[ 88102 = 2 \times 7^{2} \times 29 \times 31 \]88102 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 164160 |
| Euler totient φ(n) | 35280 |
| Square | 7761962404 |
| Cube | 683844411717208 |
| Square root | 296.819811 (= 7√1798) |
| Digit sum / digital root | 19 / 1 |
| Collatz steps to 1 | 71 |
| Scientific notation | 8.8102 × |
88102 in other forms
| Form | Value |
|---|---|
| In words | eighty-eight thousand one hundred and two |
| Binary (base 2) | 10101100000100110 |
| Octal (base 8) | 254046 |
| Hexadecimal (base 16) | 15826 |
| Base 3 | 11110212001 |
| As time | 88102 seconds = 24 h 28 min 22 s |
Is 88102 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (88102 ÷ 2 = 44051) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 2) | 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 4) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (88102 ÷ 7 = 12586) | 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 6) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 1) | 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 | No (remainder 10) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 88102 a prime number?
No. 88102 = 2 × × 29 × 31, so it is divisible by 2.
What are the factors of 88102?
1, 2, 7, 14, 29, 31, 49, 58, 62, 98, 203, 217, 406, 434, 899, 1421, 1519, 1798, 2842, 3038, 6293, 12586, 44051, 88102.
What is 88102 in binary?
10101100000100110 (hexadecimal 15826, octal 254046).
What is the square root of 88102?
About 296.8198, exactly 7√1798.
Is 88102 divisible by 3?
No. Its digits add up to 19, which is not a multiple of 3.
What is special about the number 88102?
88102 is a happy number: repeatedly adding the squares of its digits reaches 1.