The number 73164
73164 is a composite number with 48 divisors. Its prime factorisation is × 3 × 7 × 13 × 67. Divisors (48): 1, 2, 3, 4, 6, 7, 12, 13, 14, 21, 26, 28, 39, 42, 52, 67 … 73164.
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How to work it out
- 1
What is special about 73164: a Harshad number: divisible by its digit sum 21.
- 2
73164 is composite. Its prime factorisation is
- 3
The divisors add up to 213248; without 73164 itself that is 140084, so 73164 is abundant (140084 is more than 73164). Euler's totient φ(73164) = 19008 numbers up to 73164 share no factor with it.
- 4
The digits of 73164 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 68 steps to reach 1.
LaTeX source of the formulas on this page
\[ 73164 = 2^{2} \times 3 \times 7 \times 13 \times 67 \]73164 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 213248 |
| Euler totient φ(n) | 19008 |
| Square | 5352970896 |
| Cube | 391644762634944 |
| Square root | 270.488447 (= 2√18291) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 68 |
| Scientific notation | 7.3164 × |
73164 in other forms
| Form | Value |
|---|---|
| In words | seventy-three thousand one hundred and sixty-four |
| Binary (base 2) | 10001110111001100 |
| Octal (base 8) | 216714 |
| Hexadecimal (base 16) | 11DCC |
| Base 3 | 10201100210 |
| As time | 73164 seconds = 20 h 19 min 24 s |
Is 73164 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (73164 ÷ 2 = 36582) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (73164 ÷ 3 = 24388) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (73164 ÷ 4 = 18291) | 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 (73164 ÷ 6 = 12194) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (73164 ÷ 7 = 10452) | 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 | No (remainder 3) | 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 3) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (73164 ÷ 12 = 6097) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 73164 a prime number?
No. 73164 = × 3 × 7 × 13 × 67, so it is divisible by 2.
What are the factors of 73164?
1, 2, 3, 4, 6, 7, 12, 13, 14, 21, 26, 28, 39, 42, 52, 67, 78, 84, 91, 134, 156, 182, 201, 268, 273, 364, 402, 469, 546, 804, 871, 938, 1092, 1407, 1742, 1876, 2613, 2814, 3484, 5226, 5628, 6097, 10452, 12194, 18291, 24388, 36582, 73164.
What is 73164 in binary?
10001110111001100 (hexadecimal 11DCC, octal 216714).
What is the square root of 73164?
About 270.4884, exactly 2√18291.
Is 73164 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 73164?
73164 is a Harshad number: divisible by its digit sum 21.