The number 50400
50400 is a highly composite number: it has 108 divisors, more than any smaller number. Its prime factorisation is × × × 7. Divisors (108): 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20 … 50400.
Pick any whole number from 1 to 100,000.
How to work it out
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What is special about 50400: a highly composite number: it has 108 divisors, more than any smaller number; a Harshad number: divisible by its digit sum 9.
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50400 is composite. Its prime factorisation is
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The divisors add up to 203112; without 50400 itself that is 152712, so 50400 is abundant (152712 is more than 50400). Euler's totient φ(50400) = 11520 numbers up to 50400 share no factor with it.
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The digits of 50400 add up to 9, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 65 steps to reach 1.
LaTeX source of the formulas on this page
\[ 50400 = 2^{5} \times 3^{2} \times 5^{2} \times 7 \]50400 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 108 |
| Sum of divisors | 203112 |
| Euler totient φ(n) | 11520 |
| Square | 2540160000 |
| Cube | 128024064000000 |
| Square root | 224.499443 (= 60√14) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 65 |
| Scientific notation | 5.04 × |
50400 in other forms
| Form | Value |
|---|---|
| In words | fifty thousand four hundred |
| Binary (base 2) | 1100010011100000 |
| Octal (base 8) | 142340 |
| Hexadecimal (base 16) | C4E0 |
| Base 3 | 2120010200 |
| As time | 50400 seconds = 14 h 0 min 0 s |
Is 50400 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (50400 ÷ 2 = 25200) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (50400 ÷ 3 = 16800) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (50400 ÷ 4 = 12600) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (50400 ÷ 5 = 10080) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (50400 ÷ 6 = 8400) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (50400 ÷ 7 = 7200) | 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 (50400 ÷ 8 = 6300) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (50400 ÷ 9 = 5600) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (50400 ÷ 10 = 5040) | 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 | Yes (50400 ÷ 12 = 4200) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 50400 a prime number?
No. 50400 = × × × 7, so it is divisible by 2.
What are the factors of 50400?
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 25, 28, 30, 32, 35, 36, 40, 42, 45, 48, 50, 56, 60, 63, 70, 72, 75, 80, 84, 90, 96, 100, 105, 112, 120, 126, 140, 144, 150, 160, 168, 175, 180, 200, 210, 224, 225, 240, 252, 280, 288, 300, 315, 336, 350, 360, 400, 420, 450, 480, 504, 525, 560, 600, 630, 672, 700, 720, 800, 840, 900, 1008, 1050, 1120, 1200, 1260, 1400, 1440, 1575, 1680, 1800, 2016, 2100, 2400, 2520, 2800, 3150, 3360, 3600, 4200, 5040, 5600, 6300, 7200, 8400, 10080, 12600, 16800, 25200, 50400.
What is 50400 in binary?
1100010011100000 (hexadecimal C4E0, octal 142340).
What is the square root of 50400?
About 224.4994, exactly 60√14.
Is 50400 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 50400?
50400 is a highly composite number: it has 108 divisors, more than any smaller number; a Harshad number: divisible by its digit sum 9.