The number 53802
53802 is a composite number with 36 divisors. Its prime factorisation is 2 × × × 61. Divisors (36): 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 49, 61, 63, 98, 122, 126 … 53802.
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How to work it out
- 1
What is special about 53802: a Harshad number: divisible by its digit sum 18.
- 2
53802 is composite. Its prime factorisation is
- 3
The divisors add up to 137826; without 53802 itself that is 84024, so 53802 is abundant (84024 is more than 53802). Euler's totient φ(53802) = 15120 numbers up to 53802 share no factor with it.
- 4
The digits of 53802 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
\[ 53802 = 2 \times 3^{2} \times 7^{2} \times 61 \]53802 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 137826 |
| Euler totient φ(n) | 15120 |
| Square | 2894655204 |
| Cube | 155738239285608 |
| Square root | 231.952581 (= 21√122) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 47 |
| Scientific notation | 5.3802 × |
53802 in other forms
| Form | Value |
|---|---|
| In words | fifty-three thousand eight hundred and two |
| Binary (base 2) | 1101001000101010 |
| Octal (base 8) | 151052 |
| Hexadecimal (base 16) | D22A |
| Base 3 | 2201210200 |
| As time | 53802 seconds = 14 h 56 min 42 s |
Is 53802 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (53802 ÷ 2 = 26901) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (53802 ÷ 3 = 17934) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 2) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 2) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (53802 ÷ 6 = 8967) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (53802 ÷ 7 = 7686) | 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 2) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (53802 ÷ 9 = 5978) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 2) | 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 6) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 53802 a prime number?
No. 53802 = 2 × × × 61, so it is divisible by 2.
What are the factors of 53802?
1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 49, 61, 63, 98, 122, 126, 147, 183, 294, 366, 427, 441, 549, 854, 882, 1098, 1281, 2562, 2989, 3843, 5978, 7686, 8967, 17934, 26901, 53802.
What is 53802 in binary?
1101001000101010 (hexadecimal D22A, octal 151052).
What is the square root of 53802?
About 231.9526, exactly 21√122.
Is 53802 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 53802?
53802 is a Harshad number: divisible by its digit sum 18.