The number 87960
87960 is a composite number with 32 divisors. Its prime factorisation is × 3 × 5 × 733. Divisors (32): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120 … 87960.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 87960: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 30.
- 2
87960 is composite. Its prime factorisation is
- 3
The divisors add up to 264240; without 87960 itself that is 176280, so 87960 is abundant (176280 is more than 87960). Euler's totient φ(87960) = 23424 numbers up to 87960 share no factor with it.
- 4
The digits of 87960 add up to 30, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 102 steps to reach 1.
LaTeX source of the formulas on this page
\[ 87960 = 2^{3} \times 3 \times 5 \times 733 \]87960 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 264240 |
| Euler totient φ(n) | 23424 |
| Square | 7736961600 |
| Cube | 680543142336000 |
| Square root | 296.580512 (= 2√21990) |
| Digit sum / digital root | 30 / 3 |
| Collatz steps to 1 | 102 |
| Scientific notation | 8.796 × |
87960 in other forms
| Form | Value |
|---|---|
| In words | eighty-seven thousand nine hundred and sixty |
| Binary (base 2) | 10101011110011000 |
| Octal (base 8) | 253630 |
| Hexadecimal (base 16) | 15798 |
| Base 3 | 11110122210 |
| As time | 87960 seconds = 24 h 26 min 0 s |
Is 87960 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (87960 ÷ 2 = 43980) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (87960 ÷ 3 = 29320) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (87960 ÷ 4 = 21990) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (87960 ÷ 5 = 17592) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (87960 ÷ 6 = 14660) | 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 | Yes (87960 ÷ 8 = 10995) | 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 | Yes (87960 ÷ 10 = 8796) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (87960 ÷ 12 = 7330) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 87960 a prime number?
No. 87960 = × 3 × 5 × 733, so it is divisible by 2.
What are the factors of 87960?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120, 733, 1466, 2199, 2932, 3665, 4398, 5864, 7330, 8796, 10995, 14660, 17592, 21990, 29320, 43980, 87960.
What is 87960 in binary?
10101011110011000 (hexadecimal 15798, octal 253630).
What is the square root of 87960?
About 296.5805, exactly 2√21990.
Is 87960 divisible by 3?
Yes. Its digits add up to 30, a multiple of 3.
What is special about the number 87960?
87960 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 30.