The number 157
157 is the 37th prime number. Its only divisors are 1 and 157.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 157: the 37th prime number.
- 2
157 is prime, so its only factors are 1 and 157. It is the 37th prime; the next prime is 163 and the one before is 151.
- 3
The divisors add up to 158; without 157 itself that is 1, so 157 is deficient (1 is less than 157). Euler's totient φ(157) = 156 numbers up to 157 share no factor with it.
- 4
The digits of 157 add up to 13, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 36 steps to reach 1.
157 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 158 |
| Euler totient φ(n) | 156 |
| Square | 24649 |
| Cube | 3869893 |
| Square root | 12.529964 |
| Digit sum / digital root | 13 / 4 |
| Collatz steps to 1 | 36 |
| Scientific notation | 1.57 × |
157 in other forms
| Form | Value |
|---|---|
| In words | one hundred and fifty-seven |
| Roman numerals | CLVII |
| Binary (base 2) | 10011101 |
| Octal (base 8) | 235 |
| Hexadecimal (base 16) | 9D |
| Base 3 | 12211 |
| As time | 157 seconds = 2 min 37 s |
Is 157 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 1) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 2) | 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 | No (remainder 3) | 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 5) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 4) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 7) | 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 1) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 157 a prime number?
Yes. 157 is divisible only by 1 and itself.
What are the factors of 157?
1, 157.
What is 157 in binary?
10011101 (hexadecimal 9D, octal 235).
What is the square root of 157?
About 12.5300.
What is 157 in Roman numerals?
CLVII.
Is 157 divisible by 3?
No. Its digits add up to 13, which is not a multiple of 3.
What is special about the number 157?
157 is the 37th prime number.