The number 91
91 is a triangular number: 1 + 2 + … + 13 = 91. Its prime factorisation is 7 × 13. Divisors (4): 1, 7, 13, 91.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 91: a triangular number: 1 + 2 + … + 13 = 91; a happy number: repeatedly adding the squares of its digits reaches 1; a semiprime: 7 × 13, the product of two primes.
- 2
91 is composite. Its prime factorisation is
- 3
The divisors add up to 112; without 91 itself that is 21, so 91 is deficient (21 is less than 91). Euler's totient φ(91) = 72 numbers up to 91 share no factor with it.
- 4
The digits of 91 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 92 steps to reach 1.
LaTeX source of the formulas on this page
\[ 91 = 7 \times 13 \]
91 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 4 |
| Sum of divisors | 112 |
| Euler totient φ(n) | 72 |
| Square | 8281 |
| Cube | 753571 |
| Square root | 9.539392 |
| Digit sum / digital root | 10 / 1 |
| Collatz steps to 1 | 92 |
| Scientific notation | 9.1 × |
91 in other forms
| Form | Value |
|---|---|
| In words | ninety-one |
| Roman numerals | XCI |
| Binary (base 2) | 1011011 |
| Octal (base 8) | 133 |
| Hexadecimal (base 16) | 5B |
| Base 3 | 10101 |
| As time | 91 seconds = 1 min 31 s |
Is 91 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | No (remainder 1) | 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 | No (remainder 3) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 1) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 1) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (91 ÷ 7 = 13) | 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 3) | 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 | No (remainder 1) | 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 7) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 91 a prime number?
No. 91 = 7 × 13, so it is divisible by 7.
What are the factors of 91?
1, 7, 13, 91.
What is 91 in binary?
1011011 (hexadecimal 5B, octal 133).
What is the square root of 91?
About 9.5394.
What is 91 in Roman numerals?
XCI.
Is 91 divisible by 3?
No. Its digits add up to 10, which is not a multiple of 3.
What is special about the number 91?
91 is a triangular number: 1 + 2 + … + 13 = 91; a happy number: repeatedly adding the squares of its digits reaches 1; a semiprime: 7 × 13, the product of two primes.