The number 52164
52164 is a composite number with 60 divisors. Its prime factorisation is × × 7 × 23. Divisors (60): 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 23, 27, 28, 36, 42 … 52164.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 52164: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.
- 2
52164 is composite. Its prime factorisation is
- 3
The divisors add up to 162624; without 52164 itself that is 110460, so 52164 is abundant (110460 is more than 52164). Euler's totient φ(52164) = 14256 numbers up to 52164 share no factor with it.
- 4
The digits of 52164 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
\[ 52164 = 2^{2} \times 3^{4} \times 7 \times 23 \]52164 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 60 |
| Sum of divisors | 162624 |
| Euler totient φ(n) | 14256 |
| Square | 2721082896 |
| Cube | 141942568186944 |
| Square root | 228.394396 (= 18√161) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 47 |
| Scientific notation | 5.2164 × |
52164 in other forms
| Form | Value |
|---|---|
| In words | fifty-two thousand one hundred and sixty-four |
| Binary (base 2) | 1100101111000100 |
| Octal (base 8) | 145704 |
| Hexadecimal (base 16) | CBC4 |
| Base 3 | 2122120000 |
| As time | 52164 seconds = 14 h 29 min 24 s |
Is 52164 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (52164 ÷ 2 = 26082) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (52164 ÷ 3 = 17388) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (52164 ÷ 4 = 13041) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 4) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (52164 ÷ 6 = 8694) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (52164 ÷ 7 = 7452) | 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 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (52164 ÷ 9 = 5796) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 4) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 2) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (52164 ÷ 12 = 4347) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 52164 a prime number?
No. 52164 = × × 7 × 23, so it is divisible by 2.
What are the factors of 52164?
1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 23, 27, 28, 36, 42, 46, 54, 63, 69, 81, 84, 92, 108, 126, 138, 161, 162, 189, 207, 252, 276, 322, 324, 378, 414, 483, 567, 621, 644, 756, 828, 966, 1134, 1242, 1449, 1863, 1932, 2268, 2484, 2898, 3726, 4347, 5796, 7452, 8694, 13041, 17388, 26082, 52164.
What is 52164 in binary?
1100101111000100 (hexadecimal CBC4, octal 145704).
What is the square root of 52164?
About 228.3944, exactly 18√161.
Is 52164 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 52164?
52164 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.