The number 38100
38100 is a composite number with 36 divisors. Its prime factorisation is × 3 × × 127. Divisors (36): 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100 … 38100.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 38100: a Harshad number: divisible by its digit sum 12.
- 2
38100 is composite. Its prime factorisation is
- 3
The divisors add up to 111104; without 38100 itself that is 73004, so 38100 is abundant (73004 is more than 38100). Euler's totient φ(38100) = 10080 numbers up to 38100 share no factor with it.
- 4
The digits of 38100 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 80 steps to reach 1.
LaTeX source of the formulas on this page
\[ 38100 = 2^{2} \times 3 \times 5^{2} \times 127 \]38100 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 111104 |
| Euler totient φ(n) | 10080 |
| Square | 1451610000 |
| Cube | 55306341000000 |
| Square root | 195.192213 (= 10√381) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 80 |
| Scientific notation | 3.81 × |
38100 in other forms
| Form | Value |
|---|---|
| In words | thirty-eight thousand one hundred |
| Binary (base 2) | 1001010011010100 |
| Octal (base 8) | 112324 |
| Hexadecimal (base 16) | 94D4 |
| Base 3 | 1221021010 |
| As time | 38100 seconds = 10 h 35 min 0 s |
Is 38100 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (38100 ÷ 2 = 19050) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (38100 ÷ 3 = 12700) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (38100 ÷ 4 = 9525) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (38100 ÷ 5 = 7620) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (38100 ÷ 6 = 6350) | 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 | 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 | Yes (38100 ÷ 10 = 3810) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 7) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (38100 ÷ 12 = 3175) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 38100 a prime number?
No. 38100 = × 3 × × 127, so it is divisible by 2.
What are the factors of 38100?
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 127, 150, 254, 300, 381, 508, 635, 762, 1270, 1524, 1905, 2540, 3175, 3810, 6350, 7620, 9525, 12700, 19050, 38100.
What is 38100 in binary?
1001010011010100 (hexadecimal 94D4, octal 112324).
What is the square root of 38100?
About 195.1922, exactly 10√381.
Is 38100 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 38100?
38100 is a Harshad number: divisible by its digit sum 12.