The number 75120
75120 is a composite number with 40 divisors. Its prime factorisation is × 3 × 5 × 313. Divisors (40): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48 … 75120.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 75120: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 15.
- 2
75120 is composite. Its prime factorisation is
- 3
The divisors add up to 233616; without 75120 itself that is 158496, so 75120 is abundant (158496 is more than 75120). Euler's totient φ(75120) = 19968 numbers up to 75120 share no factor with it.
- 4
The digits of 75120 add up to 15, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 112 steps to reach 1.
LaTeX source of the formulas on this page
\[ 75120 = 2^{4} \times 3 \times 5 \times 313 \]75120 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 40 |
| Sum of divisors | 233616 |
| Euler totient φ(n) | 19968 |
| Square | 5643014400 |
| Cube | 423903241728000 |
| Square root | 274.080280 (= 4√4695) |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 112 |
| Scientific notation | 7.512 × |
75120 in other forms
| Form | Value |
|---|---|
| In words | seventy-five thousand one hundred and twenty |
| Binary (base 2) | 10010010101110000 |
| Octal (base 8) | 222560 |
| Hexadecimal (base 16) | 12570 |
| Base 3 | 10211001020 |
| As time | 75120 seconds = 20 h 52 min 0 s |
Is 75120 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (75120 ÷ 2 = 37560) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (75120 ÷ 3 = 25040) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (75120 ÷ 4 = 18780) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (75120 ÷ 5 = 15024) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (75120 ÷ 6 = 12520) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 (75120 ÷ 8 = 9390) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (75120 ÷ 10 = 7512) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (75120 ÷ 12 = 6260) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 75120 a prime number?
No. 75120 = × 3 × 5 × 313, so it is divisible by 2.
What are the factors of 75120?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240, 313, 626, 939, 1252, 1565, 1878, 2504, 3130, 3756, 4695, 5008, 6260, 7512, 9390, 12520, 15024, 18780, 25040, 37560, 75120.
What is 75120 in binary?
10010010101110000 (hexadecimal 12570, octal 222560).
What is the square root of 75120?
About 274.0803, exactly 4√4695.
Is 75120 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 75120?
75120 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 15.