The number 24480
24480 is a composite number with 72 divisors. Its prime factorisation is × × 5 × 17. Divisors (72): 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 17, 18, 20, 24 … 24480.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 24480: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.
- 2
24480 is composite. Its prime factorisation is
- 3
The divisors add up to 88452; without 24480 itself that is 63972, so 24480 is abundant (63972 is more than 24480). Euler's totient φ(24480) = 6144 numbers up to 24480 share no factor with it.
- 4
The digits of 24480 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 51 steps to reach 1.
LaTeX source of the formulas on this page
\[ 24480 = 2^{5} \times 3^{2} \times 5 \times 17 \]24480 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 72 |
| Sum of divisors | 88452 |
| Euler totient φ(n) | 6144 |
| Square | 599270400 |
| Cube | 14670139392000 |
| Square root | 156.460858 (= 12√170) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 51 |
| Scientific notation | 2.448 × |
24480 in other forms
| Form | Value |
|---|---|
| In words | twenty-four thousand four hundred and eighty |
| Binary (base 2) | 101111110100000 |
| Octal (base 8) | 57640 |
| Hexadecimal (base 16) | 5FA0 |
| Base 3 | 1020120200 |
| As time | 24480 seconds = 6 h 48 min 0 s |
Is 24480 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (24480 ÷ 2 = 12240) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (24480 ÷ 3 = 8160) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (24480 ÷ 4 = 6120) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (24480 ÷ 5 = 4896) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (24480 ÷ 6 = 4080) | 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 (24480 ÷ 8 = 3060) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (24480 ÷ 9 = 2720) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (24480 ÷ 10 = 2448) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 5) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (24480 ÷ 12 = 2040) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 24480 a prime number?
No. 24480 = × × 5 × 17, so it is divisible by 2.
What are the factors of 24480?
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 17, 18, 20, 24, 30, 32, 34, 36, 40, 45, 48, 51, 60, 68, 72, 80, 85, 90, 96, 102, 120, 136, 144, 153, 160, 170, 180, 204, 240, 255, 272, 288, 306, 340, 360, 408, 480, 510, 544, 612, 680, 720, 765, 816, 1020, 1224, 1360, 1440, 1530, 1632, 2040, 2448, 2720, 3060, 4080, 4896, 6120, 8160, 12240, 24480.
What is 24480 in binary?
101111110100000 (hexadecimal 5FA0, octal 57640).
What is the square root of 24480?
About 156.4609, exactly 12√170.
Is 24480 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 24480?
24480 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.