The number 46800
46800 is a composite number with 90 divisors. Its prime factorisation is × × × 13. Divisors (90): 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 15, 16, 18, 20, 24 … 46800.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 46800: a Harshad number: divisible by its digit sum 18.
- 2
46800 is composite. Its prime factorisation is
- 3
The divisors add up to 174902; without 46800 itself that is 128102, so 46800 is abundant (128102 is more than 46800). Euler's totient φ(46800) = 11520 numbers up to 46800 share no factor with it.
- 4
The digits of 46800 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 145 steps to reach 1.
LaTeX source of the formulas on this page
\[ 46800 = 2^{4} \times 3^{2} \times 5^{2} \times 13 \]46800 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 90 |
| Sum of divisors | 174902 |
| Euler totient φ(n) | 11520 |
| Square | 2190240000 |
| Cube | 102503232000000 |
| Square root | 216.333077 (= 60√13) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 145 |
| Scientific notation | 4.68 × |
46800 in other forms
| Form | Value |
|---|---|
| In words | forty-six thousand eight hundred |
| Binary (base 2) | 1011011011010000 |
| Octal (base 8) | 133320 |
| Hexadecimal (base 16) | B6D0 |
| Base 3 | 2101012100 |
| As time | 46800 seconds = 13 h 0 min 0 s |
Is 46800 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (46800 ÷ 2 = 23400) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (46800 ÷ 3 = 15600) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (46800 ÷ 4 = 11700) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (46800 ÷ 5 = 9360) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (46800 ÷ 6 = 7800) | 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 | Yes (46800 ÷ 8 = 5850) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (46800 ÷ 9 = 5200) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (46800 ÷ 10 = 4680) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (46800 ÷ 12 = 3900) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 46800 a prime number?
No. 46800 = × × × 13, so it is divisible by 2.
What are the factors of 46800?
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 15, 16, 18, 20, 24, 25, 26, 30, 36, 39, 40, 45, 48, 50, 52, 60, 65, 72, 75, 78, 80, 90, 100, 104, 117, 120, 130, 144, 150, 156, 180, 195, 200, 208, 225, 234, 240, 260, 300, 312, 325, 360, 390, 400, 450, 468, 520, 585, 600, 624, 650, 720, 780, 900, 936, 975, 1040, 1170, 1200, 1300, 1560, 1800, 1872, 1950, 2340, 2600, 2925, 3120, 3600, 3900, 4680, 5200, 5850, 7800, 9360, 11700, 15600, 23400, 46800.
What is 46800 in binary?
1011011011010000 (hexadecimal B6D0, octal 133320).
What is the square root of 46800?
About 216.3331, exactly 60√13.
Is 46800 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 46800?
46800 is a Harshad number: divisible by its digit sum 18.