The number 87204
87204 is a composite number with 36 divisors. Its prime factorisation is × 3 × × 43. Divisors (36): 1, 2, 3, 4, 6, 12, 13, 26, 39, 43, 52, 78, 86, 129, 156, 169 … 87204.
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How to work it out
- 1
What is special about 87204: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
87204 is composite. Its prime factorisation is
- 3
The divisors add up to 225456; without 87204 itself that is 138252, so 87204 is abundant (138252 is more than 87204). Euler's totient φ(87204) = 26208 numbers up to 87204 share no factor with it.
- 4
The digits of 87204 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 151 steps to reach 1.
LaTeX source of the formulas on this page
\[ 87204 = 2^{2} \times 3 \times 13^{2} \times 43 \]87204 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 225456 |
| Euler totient φ(n) | 26208 |
| Square | 7604537616 |
| Cube | 663146098265664 |
| Square root | 295.303234 (= 26√129) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 151 |
| Scientific notation | 8.7204 × |
87204 in other forms
| Form | Value |
|---|---|
| In words | eighty-seven thousand two hundred and four |
| Binary (base 2) | 10101010010100100 |
| Octal (base 8) | 252244 |
| Hexadecimal (base 16) | 154A4 |
| Base 3 | 11102121210 |
| As time | 87204 seconds = 24 h 13 min 24 s |
Is 87204 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (87204 ÷ 2 = 43602) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (87204 ÷ 3 = 29068) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (87204 ÷ 4 = 21801) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 4) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (87204 ÷ 6 = 14534) | 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 3) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 4) | 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 | Yes (87204 ÷ 12 = 7267) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 87204 a prime number?
No. 87204 = × 3 × × 43, so it is divisible by 2.
What are the factors of 87204?
1, 2, 3, 4, 6, 12, 13, 26, 39, 43, 52, 78, 86, 129, 156, 169, 172, 258, 338, 507, 516, 559, 676, 1014, 1118, 1677, 2028, 2236, 3354, 6708, 7267, 14534, 21801, 29068, 43602, 87204.
What is 87204 in binary?
10101010010100100 (hexadecimal 154A4, octal 252244).
What is the square root of 87204?
About 295.3032, exactly 26√129.
Is 87204 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 87204?
87204 is a happy number: repeatedly adding the squares of its digits reaches 1.