The number 74880
74880 is a composite number with 96 divisors. Its prime factorisation is × × 5 × 13. Divisors (96): 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 15, 16, 18, 20, 24 … 74880.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 74880: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
74880 is composite. Its prime factorisation is
- 3
The divisors add up to 278460; without 74880 itself that is 203580, so 74880 is abundant (203580 is more than 74880). Euler's totient φ(74880) = 18432 numbers up to 74880 share no factor with it.
- 4
The digits of 74880 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 63 steps to reach 1.
LaTeX source of the formulas on this page
\[ 74880 = 2^{7} \times 3^{2} \times 5 \times 13 \]74880 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 96 |
| Sum of divisors | 278460 |
| Euler totient φ(n) | 18432 |
| Square | 5607014400 |
| Cube | 419853238272000 |
| Square root | 273.642102 (= 24√130) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 63 |
| Scientific notation | 7.488 × |
74880 in other forms
| Form | Value |
|---|---|
| In words | seventy-four thousand eight hundred and eighty |
| Binary (base 2) | 10010010010000000 |
| Octal (base 8) | 222200 |
| Hexadecimal (base 16) | 12480 |
| Base 3 | 10210201100 |
| As time | 74880 seconds = 20 h 48 min 0 s |
Is 74880 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (74880 ÷ 2 = 37440) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (74880 ÷ 3 = 24960) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (74880 ÷ 4 = 18720) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (74880 ÷ 5 = 14976) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (74880 ÷ 6 = 12480) | 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 (74880 ÷ 8 = 9360) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (74880 ÷ 9 = 8320) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (74880 ÷ 10 = 7488) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 3) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (74880 ÷ 12 = 6240) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 74880 a prime number?
No. 74880 = × × 5 × 13, so it is divisible by 2.
What are the factors of 74880?
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 15, 16, 18, 20, 24, 26, 30, 32, 36, 39, 40, 45, 48, 52, 60, 64, 65, 72, 78, 80, 90, 96, 104, 117, 120, 128, 130, 144, 156, 160, 180, 192, 195, 208, 234, 240, 260, 288, 312, 320, 360, 384, 390, 416, 468, 480, 520, 576, 585, 624, 640, 720, 780, 832, 936, 960, 1040, 1152, 1170, 1248, 1440, 1560, 1664, 1872, 1920, 2080, 2340, 2496, 2880, 3120, 3744, 4160, 4680, 4992, 5760, 6240, 7488, 8320, 9360, 12480, 14976, 18720, 24960, 37440, 74880.
What is 74880 in binary?
10010010010000000 (hexadecimal 12480, octal 222200).
What is the square root of 74880?
About 273.6421, exactly 24√130.
Is 74880 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 74880?
74880 is a happy number: repeatedly adding the squares of its digits reaches 1.