The number 4100
4100 is a composite number with 18 divisors. Its prime factorisation is × × 41. Divisors (18): 1, 2, 4, 5, 10, 20, 25, 41, 50, 82, 100, 164, 205, 410, 820, 1025 … 4100.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 4100: a Harshad number: divisible by its digit sum 5.
- 2
4100 is composite. Its prime factorisation is
- 3
The divisors add up to 9114; without 4100 itself that is 5014, so 4100 is abundant (5014 is more than 4100). Euler's totient φ(4100) = 1600 numbers up to 4100 share no factor with it.
- 4
The digits of 4100 add up to 5, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 38 steps to reach 1.
LaTeX source of the formulas on this page
\[ 4100 = 2^{2} \times 5^{2} \times 41 \]4100 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 18 |
| Sum of divisors | 9114 |
| Euler totient φ(n) | 1600 |
| Square | 16810000 |
| Cube | 68921000000 |
| Square root | 64.031242 (= 10√41) |
| Digit sum / digital root | 5 / 5 |
| Collatz steps to 1 | 38 |
| Scientific notation | 4.1 × |
4100 in other forms
| Form | Value |
|---|---|
| In words | four thousand one hundred |
| Binary (base 2) | 1000000000100 |
| Octal (base 8) | 10004 |
| Hexadecimal (base 16) | 1004 |
| Base 3 | 12121212 |
| As time | 4100 seconds = 1 h 8 min 20 s |
Is 4100 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (4100 ÷ 2 = 2050) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (4100 ÷ 4 = 1025) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (4100 ÷ 5 = 820) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 2) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 5) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (4100 ÷ 10 = 410) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 8) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 4100 a prime number?
No. 4100 = × × 41, so it is divisible by 2.
What are the factors of 4100?
1, 2, 4, 5, 10, 20, 25, 41, 50, 82, 100, 164, 205, 410, 820, 1025, 2050, 4100.
What is 4100 in binary?
1000000000100 (hexadecimal 1004, octal 10004).
What is the square root of 4100?
About 64.0312, exactly 10√41.
Is 4100 divisible by 3?
No. Its digits add up to 5, which is not a multiple of 3.
What is special about the number 4100?
4100 is a Harshad number: divisible by its digit sum 5.