The number 10900
10900 is a composite number with 18 divisors. Its prime factorisation is × × 109. Divisors (18): 1, 2, 4, 5, 10, 20, 25, 50, 100, 109, 218, 436, 545, 1090, 2180, 2725 … 10900.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 10900: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 10.
- 2
10900 is composite. Its prime factorisation is
- 3
The divisors add up to 23870; without 10900 itself that is 12970, so 10900 is abundant (12970 is more than 10900). Euler's totient φ(10900) = 4320 numbers up to 10900 share no factor with it.
- 4
The digits of 10900 add up to 10, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 68 steps to reach 1.
LaTeX source of the formulas on this page
\[ 10900 = 2^{2} \times 5^{2} \times 109 \]10900 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 18 |
| Sum of divisors | 23870 |
| Euler totient φ(n) | 4320 |
| Square | 118810000 |
| Cube | 1295029000000 |
| Square root | 104.403065 (= 10√109) |
| Digit sum / digital root | 10 / 1 |
| Collatz steps to 1 | 68 |
| Scientific notation | 1.09 × |
10900 in other forms
| Form | Value |
|---|---|
| In words | ten thousand nine hundred |
| Binary (base 2) | 10101010010100 |
| Octal (base 8) | 25224 |
| Hexadecimal (base 16) | 2A94 |
| Base 3 | 112221201 |
| As time | 10900 seconds = 3 h 1 min 40 s |
Is 10900 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (10900 ÷ 2 = 5450) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (10900 ÷ 4 = 2725) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (10900 ÷ 5 = 2180) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 4) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 1) | 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 1) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (10900 ÷ 10 = 1090) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 10) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 10900 a prime number?
No. 10900 = × × 109, so it is divisible by 2.
What are the factors of 10900?
1, 2, 4, 5, 10, 20, 25, 50, 100, 109, 218, 436, 545, 1090, 2180, 2725, 5450, 10900.
What is 10900 in binary?
10101010010100 (hexadecimal 2A94, octal 25224).
What is the square root of 10900?
About 104.4031, exactly 10√109.
Is 10900 divisible by 3?
No. Its digits add up to 10, which is not a multiple of 3.
What is special about the number 10900?
10900 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 10.