The number 75180
75180 is a composite number with 48 divisors. Its prime factorisation is × 3 × 5 × 7 × 179. Divisors (48): 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35 … 75180.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 75180: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 21.
- 2
75180 is composite. Its prime factorisation is
- 3
The divisors add up to 241920; without 75180 itself that is 166740, so 75180 is abundant (166740 is more than 75180). Euler's totient φ(75180) = 17088 numbers up to 75180 share no factor with it.
- 4
The digits of 75180 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 156 steps to reach 1.
LaTeX source of the formulas on this page
\[ 75180 = 2^{2} \times 3 \times 5 \times 7 \times 179 \]75180 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 241920 |
| Euler totient φ(n) | 17088 |
| Square | 5652032400 |
| Cube | 424919795832000 |
| Square root | 274.189715 (= 2√18795) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 156 |
| Scientific notation | 7.518 × |
75180 in other forms
| Form | Value |
|---|---|
| In words | seventy-five thousand one hundred and eighty |
| Binary (base 2) | 10010010110101100 |
| Octal (base 8) | 222654 |
| Hexadecimal (base 16) | 125AC |
| Base 3 | 10211010110 |
| As time | 75180 seconds = 20 h 53 min 0 s |
Is 75180 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (75180 ÷ 2 = 37590) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (75180 ÷ 3 = 25060) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (75180 ÷ 4 = 18795) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (75180 ÷ 5 = 15036) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (75180 ÷ 6 = 12530) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (75180 ÷ 7 = 10740) | 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 | Yes (75180 ÷ 10 = 7518) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (75180 ÷ 12 = 6265) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 75180 a prime number?
No. 75180 = × 3 × 5 × 7 × 179, so it is divisible by 2.
What are the factors of 75180?
1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 179, 210, 358, 420, 537, 716, 895, 1074, 1253, 1790, 2148, 2506, 2685, 3580, 3759, 5012, 5370, 6265, 7518, 10740, 12530, 15036, 18795, 25060, 37590, 75180.
What is 75180 in binary?
10010010110101100 (hexadecimal 125AC, octal 222654).
What is the square root of 75180?
About 274.1897, exactly 2√18795.
Is 75180 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 75180?
75180 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 21.