The number 10100
10100 is a composite number with 18 divisors. Its prime factorisation is × × 101. Divisors (18): 1, 2, 4, 5, 10, 20, 25, 50, 100, 101, 202, 404, 505, 1010, 2020, 2525 … 10100.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 10100: a Harshad number: divisible by its digit sum 2.
- 2
10100 is composite. Its prime factorisation is
- 3
The divisors add up to 22134; without 10100 itself that is 12034, so 10100 is abundant (12034 is more than 10100). Euler's totient φ(10100) = 4000 numbers up to 10100 share no factor with it.
- 4
The digits of 10100 add up to 2, and repeating that until one digit is left gives the digital root 2. The Collatz sequence (halve if even, else 3n+1) takes 42 steps to reach 1.
LaTeX source of the formulas on this page
\[ 10100 = 2^{2} \times 5^{2} \times 101 \]10100 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 18 |
| Sum of divisors | 22134 |
| Euler totient φ(n) | 4000 |
| Square | 102010000 |
| Cube | 1030301000000 |
| Square root | 100.498756 (= 10√101) |
| Digit sum / digital root | 2 / 2 |
| Collatz steps to 1 | 42 |
| Scientific notation | 1.01 × |
10100 in other forms
| Form | Value |
|---|---|
| In words | ten thousand one hundred |
| Binary (base 2) | 10011101110100 |
| Octal (base 8) | 23564 |
| Hexadecimal (base 16) | 2774 |
| Base 3 | 111212002 |
| As time | 10100 seconds = 2 h 48 min 20 s |
Is 10100 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (10100 ÷ 2 = 5050) | 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 (10100 ÷ 4 = 2525) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (10100 ÷ 5 = 2020) | 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 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 2) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (10100 ÷ 10 = 1010) | 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 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 10100 a prime number?
No. 10100 = × × 101, so it is divisible by 2.
What are the factors of 10100?
1, 2, 4, 5, 10, 20, 25, 50, 100, 101, 202, 404, 505, 1010, 2020, 2525, 5050, 10100.
What is 10100 in binary?
10011101110100 (hexadecimal 2774, octal 23564).
What is the square root of 10100?
About 100.4988, exactly 10√101.
Is 10100 divisible by 3?
No. Its digits add up to 2, which is not a multiple of 3.
What is special about the number 10100?
10100 is a Harshad number: divisible by its digit sum 2.