The number 10164
10164 is a composite number with 36 divisors. Its prime factorisation is × 3 × 7 × . Divisors (36): 1, 2, 3, 4, 6, 7, 11, 12, 14, 21, 22, 28, 33, 42, 44, 66 … 10164.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 10164: a Harshad number: divisible by its digit sum 12.
- 2
10164 is composite. Its prime factorisation is
- 3
The divisors add up to 29792; without 10164 itself that is 19628, so 10164 is abundant (19628 is more than 10164). Euler's totient φ(10164) = 2640 numbers up to 10164 share no factor with it.
- 4
The digits of 10164 add up to 12, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 34 steps to reach 1.
LaTeX source of the formulas on this page
\[ 10164 = 2^{2} \times 3 \times 7 \times 11^{2} \]10164 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 29792 |
| Euler totient φ(n) | 2640 |
| Square | 103306896 |
| Cube | 1050011290944 |
| Square root | 100.816665 (= 22√21) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 34 |
| Scientific notation | 1.0164 × |
10164 in other forms
| Form | Value |
|---|---|
| In words | ten thousand one hundred and sixty-four |
| Binary (base 2) | 10011110110100 |
| Octal (base 8) | 23664 |
| Hexadecimal (base 16) | 27B4 |
| Base 3 | 111221110 |
| As time | 10164 seconds = 2 h 49 min 24 s |
Is 10164 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (10164 ÷ 2 = 5082) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (10164 ÷ 3 = 3388) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (10164 ÷ 4 = 2541) | 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 (10164 ÷ 6 = 1694) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (10164 ÷ 7 = 1452) | 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 | Yes (10164 ÷ 11 = 924) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (10164 ÷ 12 = 847) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 10164 a prime number?
No. 10164 = × 3 × 7 × , so it is divisible by 2.
What are the factors of 10164?
1, 2, 3, 4, 6, 7, 11, 12, 14, 21, 22, 28, 33, 42, 44, 66, 77, 84, 121, 132, 154, 231, 242, 308, 363, 462, 484, 726, 847, 924, 1452, 1694, 2541, 3388, 5082, 10164.
What is 10164 in binary?
10011110110100 (hexadecimal 27B4, octal 23664).
What is the square root of 10164?
About 100.8167, exactly 22√21.
Is 10164 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 10164?
10164 is a Harshad number: divisible by its digit sum 12.