The number 53640
53640 is a composite number with 48 divisors. Its prime factorisation is × × 5 × 149. Divisors (48): 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36 … 53640.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 53640: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.
- 2
53640 is composite. Its prime factorisation is
- 3
The divisors add up to 175500; without 53640 itself that is 121860, so 53640 is abundant (121860 is more than 53640). Euler's totient φ(53640) = 14208 numbers up to 53640 share no factor with it.
- 4
The digits of 53640 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 47 steps to reach 1.
LaTeX source of the formulas on this page
\[ 53640 = 2^{3} \times 3^{2} \times 5 \times 149 \]53640 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 175500 |
| Euler totient φ(n) | 14208 |
| Square | 2877249600 |
| Cube | 154335668544000 |
| Square root | 231.603109 (= 6√1490) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 47 |
| Scientific notation | 5.364 × |
53640 in other forms
| Form | Value |
|---|---|
| In words | fifty-three thousand six hundred and forty |
| Binary (base 2) | 1101000110001000 |
| Octal (base 8) | 150610 |
| Hexadecimal (base 16) | D188 |
| Base 3 | 2201120200 |
| As time | 53640 seconds = 14 h 54 min 0 s |
Is 53640 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (53640 ÷ 2 = 26820) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (53640 ÷ 3 = 17880) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (53640 ÷ 4 = 13410) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (53640 ÷ 5 = 10728) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (53640 ÷ 6 = 8940) | 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 (53640 ÷ 8 = 6705) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (53640 ÷ 9 = 5960) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (53640 ÷ 10 = 5364) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (53640 ÷ 12 = 4470) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 53640 a prime number?
No. 53640 = × × 5 × 149, so it is divisible by 2.
What are the factors of 53640?
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 149, 180, 298, 360, 447, 596, 745, 894, 1192, 1341, 1490, 1788, 2235, 2682, 2980, 3576, 4470, 5364, 5960, 6705, 8940, 10728, 13410, 17880, 26820, 53640.
What is 53640 in binary?
1101000110001000 (hexadecimal D188, octal 150610).
What is the square root of 53640?
About 231.6031, exactly 6√1490.
Is 53640 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 53640?
53640 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.