The number 87480
87480 is a composite number with 64 divisors. Its prime factorisation is × × 5. Divisors (64): 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 27, 30 … 87480.
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How to work it out
- 1
What is special about 87480: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 27.
- 2
87480 is composite. Its prime factorisation is
- 3
The divisors add up to 295200; without 87480 itself that is 207720, so 87480 is abundant (207720 is more than 87480). Euler's totient φ(87480) = 23328 numbers up to 87480 share no factor with it.
- 4
The digits of 87480 add up to 27, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 120 steps to reach 1.
LaTeX source of the formulas on this page
\[ 87480 = 2^{3} \times 3^{7} \times 5 \]87480 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 64 |
| Sum of divisors | 295200 |
| Euler totient φ(n) | 23328 |
| Square | 7652750400 |
| Cube | 669462604992000 |
| Square root | 295.770181 (= 54√30) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 120 |
| Scientific notation | 8.748 × |
87480 in other forms
| Form | Value |
|---|---|
| In words | eighty-seven thousand four hundred and eighty |
| Binary (base 2) | 10101010110111000 |
| Octal (base 8) | 252670 |
| Hexadecimal (base 16) | 155B8 |
| Base 3 | 11110000000 |
| As time | 87480 seconds = 24 h 18 min 0 s |
Is 87480 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (87480 ÷ 2 = 43740) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (87480 ÷ 3 = 29160) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (87480 ÷ 4 = 21870) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (87480 ÷ 5 = 17496) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (87480 ÷ 6 = 14580) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 1) | 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 (87480 ÷ 8 = 10935) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (87480 ÷ 9 = 9720) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (87480 ÷ 10 = 8748) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 8) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (87480 ÷ 12 = 7290) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 87480 a prime number?
No. 87480 = × × 5, so it is divisible by 2.
What are the factors of 87480?
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 27, 30, 36, 40, 45, 54, 60, 72, 81, 90, 108, 120, 135, 162, 180, 216, 243, 270, 324, 360, 405, 486, 540, 648, 729, 810, 972, 1080, 1215, 1458, 1620, 1944, 2187, 2430, 2916, 3240, 3645, 4374, 4860, 5832, 7290, 8748, 9720, 10935, 14580, 17496, 21870, 29160, 43740, 87480.
What is 87480 in binary?
10101010110111000 (hexadecimal 155B8, octal 252670).
What is the square root of 87480?
About 295.7702, exactly 54√30.
Is 87480 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 87480?
87480 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 27.