The number 91000
91000 is a composite number with 64 divisors. Its prime factorisation is × × 7 × 13. Divisors (64): 1, 2, 4, 5, 7, 8, 10, 13, 14, 20, 25, 26, 28, 35, 40, 50 … 91000.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 91000: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 10.
- 2
91000 is composite. Its prime factorisation is
- 3
The divisors add up to 262080; without 91000 itself that is 171080, so 91000 is abundant (171080 is more than 91000). Euler's totient φ(91000) = 28800 numbers up to 91000 share no factor with it.
- 4
The digits of 91000 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 84 steps to reach 1.
LaTeX source of the formulas on this page
\[ 91000 = 2^{3} \times 5^{3} \times 7 \times 13 \]91000 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 64 |
| Sum of divisors | 262080 |
| Euler totient φ(n) | 28800 |
| Square | 8281000000 |
| Cube | 753571000000000 |
| Square root | 301.662063 (= 10√910) |
| Digit sum / digital root | 10 / 1 |
| Collatz steps to 1 | 84 |
| Scientific notation | 9.1 × |
91000 in other forms
| Form | Value |
|---|---|
| In words | ninety-one thousand |
| Binary (base 2) | 10110001101111000 |
| Octal (base 8) | 261570 |
| Hexadecimal (base 16) | 16378 |
| Base 3 | 11121211101 |
| As time | 91000 seconds = 25 h 16 min 40 s |
Is 91000 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (91000 ÷ 2 = 45500) | 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 (91000 ÷ 4 = 22750) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (91000 ÷ 5 = 18200) | 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 (91000 ÷ 7 = 13000) | 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 | Yes (91000 ÷ 8 = 11375) | 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 (91000 ÷ 10 = 9100) | 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 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 91000 a prime number?
No. 91000 = × × 7 × 13, so it is divisible by 2.
What are the factors of 91000?
1, 2, 4, 5, 7, 8, 10, 13, 14, 20, 25, 26, 28, 35, 40, 50, 52, 56, 65, 70, 91, 100, 104, 125, 130, 140, 175, 182, 200, 250, 260, 280, 325, 350, 364, 455, 500, 520, 650, 700, 728, 875, 910, 1000, 1300, 1400, 1625, 1750, 1820, 2275, 2600, 3250, 3500, 3640, 4550, 6500, 7000, 9100, 11375, 13000, 18200, 22750, 45500, 91000.
What is 91000 in binary?
10110001101111000 (hexadecimal 16378, octal 261570).
What is the square root of 91000?
About 301.6621, exactly 10√910.
Is 91000 divisible by 3?
No. Its digits add up to 10, which is not a multiple of 3.
What is special about the number 91000?
91000 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 10.