The number 9100
9100 is a composite number with 36 divisors. Its prime factorisation is × × 7 × 13. Divisors (36): 1, 2, 4, 5, 7, 10, 13, 14, 20, 25, 26, 28, 35, 50, 52, 65 … 9100.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 9100: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 10.
- 2
9100 is composite. Its prime factorisation is
- 3
The divisors add up to 24304; without 9100 itself that is 15204, so 9100 is abundant (15204 is more than 9100). Euler's totient φ(9100) = 2880 numbers up to 9100 share no factor with it.
- 4
The digits of 9100 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 21 steps to reach 1.
LaTeX source of the formulas on this page
\[ 9100 = 2^{2} \times 5^{2} \times 7 \times 13 \]9100 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 24304 |
| Euler totient φ(n) | 2880 |
| Square | 82810000 |
| Cube | 753571000000 |
| Square root | 95.393920 (= 10√91) |
| Digit sum / digital root | 10 / 1 |
| Collatz steps to 1 | 21 |
| Scientific notation | 9.1 × |
9100 in other forms
| Form | Value |
|---|---|
| In words | nine thousand one hundred |
| Binary (base 2) | 10001110001100 |
| Octal (base 8) | 21614 |
| Hexadecimal (base 16) | 238C |
| Base 3 | 110111001 |
| As time | 9100 seconds = 2 h 31 min 40 s |
Is 9100 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (9100 ÷ 2 = 4550) | 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 (9100 ÷ 4 = 2275) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (9100 ÷ 5 = 1820) | 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 | Yes (9100 ÷ 7 = 1300) | 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 (9100 ÷ 10 = 910) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 3) | 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 9100 a prime number?
No. 9100 = × × 7 × 13, so it is divisible by 2.
What are the factors of 9100?
1, 2, 4, 5, 7, 10, 13, 14, 20, 25, 26, 28, 35, 50, 52, 65, 70, 91, 100, 130, 140, 175, 182, 260, 325, 350, 364, 455, 650, 700, 910, 1300, 1820, 2275, 4550, 9100.
What is 9100 in binary?
10001110001100 (hexadecimal 238C, octal 21614).
What is the square root of 9100?
About 95.3939, exactly 10√91.
Is 9100 divisible by 3?
No. Its digits add up to 10, which is not a multiple of 3.
What is special about the number 9100?
9100 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 10.