The number 460
460 is a composite number with 12 divisors. Its prime factorisation is × 5 × 23. Divisors (12): 1, 2, 4, 5, 10, 20, 23, 46, 92, 115, 230, 460.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 460: a Harshad number: divisible by its digit sum 10.
- 2
460 is composite. Its prime factorisation is
- 3
The divisors add up to 1008; without 460 itself that is 548, so 460 is abundant (548 is more than 460). Euler's totient φ(460) = 176 numbers up to 460 share no factor with it.
- 4
The digits of 460 add up to 10, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 35 steps to reach 1.
LaTeX source of the formulas on this page
\[ 460 = 2^{2} \times 5 \times 23 \]460 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 1008 |
| Euler totient φ(n) | 176 |
| Square | 211600 |
| Cube | 97336000 |
| Square root | 21.447611 (= 2√115) |
| Digit sum / digital root | 10 / 1 |
| Collatz steps to 1 | 35 |
| Scientific notation | 4.6 × |
460 in other forms
| Form | Value |
|---|---|
| In words | four hundred and sixty |
| Roman numerals | CDLX |
| Binary (base 2) | 111001100 |
| Octal (base 8) | 714 |
| Hexadecimal (base 16) | 1CC |
| Base 3 | 122001 |
| As time | 460 seconds = 7 min 40 s |
Is 460 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (460 ÷ 2 = 230) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (460 ÷ 4 = 115) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (460 ÷ 5 = 92) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 4) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 1) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (460 ÷ 10 = 46) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 9) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 460 a prime number?
No. 460 = × 5 × 23, so it is divisible by 2.
What are the factors of 460?
1, 2, 4, 5, 10, 20, 23, 46, 92, 115, 230, 460.
What is 460 in binary?
111001100 (hexadecimal 1CC, octal 714).
What is the square root of 460?
About 21.4476, exactly 2√115.
What is 460 in Roman numerals?
CDLX.
Is 460 divisible by 3?
No. Its digits add up to 10, which is not a multiple of 3.
What is special about the number 460?
460 is a Harshad number: divisible by its digit sum 10.