The number 480
480 is a composite number with 24 divisors. Its prime factorisation is × 3 × 5. Divisors (24): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40 … 480.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 480: a Harshad number: divisible by its digit sum 12.
- 2
480 is composite. Its prime factorisation is
- 3
The divisors add up to 1512; without 480 itself that is 1032, so 480 is abundant (1032 is more than 480). Euler's totient φ(480) = 128 numbers up to 480 share no factor with it.
- 4
The digits of 480 add up to 12, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 22 steps to reach 1.
LaTeX source of the formulas on this page
\[ 480 = 2^{5} \times 3 \times 5 \]480 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 1512 |
| Euler totient φ(n) | 128 |
| Square | 230400 |
| Cube | 110592000 |
| Square root | 21.908902 (= 4√30) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 22 |
| Scientific notation | 4.8 × |
480 in other forms
| Form | Value |
|---|---|
| In words | four hundred and eighty |
| Roman numerals | CDLXXX |
| Binary (base 2) | 111100000 |
| Octal (base 8) | 740 |
| Hexadecimal (base 16) | 1E0 |
| Base 3 | 122210 |
| As time | 480 seconds = 8 min 0 s |
Is 480 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (480 ÷ 2 = 240) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (480 ÷ 3 = 160) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (480 ÷ 4 = 120) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (480 ÷ 5 = 96) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (480 ÷ 6 = 80) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 (480 ÷ 8 = 60) | 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 (480 ÷ 10 = 48) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 7) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (480 ÷ 12 = 40) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 480 a prime number?
No. 480 = × 3 × 5, so it is divisible by 2.
What are the factors of 480?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 80, 96, 120, 160, 240, 480.
What is 480 in binary?
111100000 (hexadecimal 1E0, octal 740).
What is the square root of 480?
About 21.9089, exactly 4√30.
What is 480 in Roman numerals?
CDLXXX.
Is 480 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 480?
480 is a Harshad number: divisible by its digit sum 12.