The number 496
496 is a perfect number: its divisors below itself add up to 496 and a triangular number: 1 + 2 + … + 31 = 496. Its prime factorisation is × 31. Divisors (10): 1, 2, 4, 8, 16, 31, 62, 124, 248, 496.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 496: a perfect number: its divisors below itself add up to 496; a triangular number: 1 + 2 + … + 31 = 496; a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
496 is composite. Its prime factorisation is
- 3
The divisors add up to 992; without 496 itself that is 496, so 496 is a perfect number. Euler's totient φ(496) = 240 numbers up to 496 share no factor with it.
- 4
The digits of 496 add up to 19, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 110 steps to reach 1.
LaTeX source of the formulas on this page
\[ 496 = 2^{4} \times 31 \]496 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 10 |
| Sum of divisors | 992 |
| Euler totient φ(n) | 240 |
| Square | 246016 |
| Cube | 122023936 |
| Square root | 22.271057 (= 4√31) |
| Digit sum / digital root | 19 / 1 |
| Collatz steps to 1 | 110 |
| Scientific notation | 4.96 × |
496 in other forms
| Form | Value |
|---|---|
| In words | four hundred and ninety-six |
| Roman numerals | CDXCVI |
| Binary (base 2) | 111110000 |
| Octal (base 8) | 760 |
| Hexadecimal (base 16) | 1F0 |
| Base 3 | 200101 |
| As time | 496 seconds = 8 min 16 s |
Is 496 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (496 ÷ 2 = 248) | 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 (496 ÷ 4 = 124) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 1) | 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 6) | 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 (496 ÷ 8 = 62) | 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 | No (remainder 6) | 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 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 496 a prime number?
No. 496 = × 31, so it is divisible by 2.
What are the factors of 496?
1, 2, 4, 8, 16, 31, 62, 124, 248, 496.
What is 496 in binary?
111110000 (hexadecimal 1F0, octal 760).
What is the square root of 496?
About 22.2711, exactly 4√31.
What is 496 in Roman numerals?
CDXCVI.
Is 496 divisible by 3?
No. Its digits add up to 19, which is not a multiple of 3.
What is special about the number 496?
496 is a perfect number: its divisors below itself add up to 496; a triangular number: 1 + 2 + … + 31 = 496; a happy number: repeatedly adding the squares of its digits reaches 1.