The number 153
153 is an Armstrong number: each digit raised to the power 3 adds up to 153, a triangular number: 1 + 2 + … + 17 = 153 and a binary palindrome (10011001). Its prime factorisation is × 17. Divisors (6): 1, 3, 9, 17, 51, 153.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 153: an Armstrong number: each digit raised to the power 3 adds up to 153; a triangular number: 1 + 2 + … + 17 = 153; a binary palindrome (10011001); a Harshad number: divisible by its digit sum 9.
- 2
153 is composite. Its prime factorisation is
- 3
The divisors add up to 234; without 153 itself that is 81, so 153 is deficient (81 is less than 153). Euler's totient φ(153) = 96 numbers up to 153 share no factor with it.
- 4
The digits of 153 add up to 9, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 36 steps to reach 1.
LaTeX source of the formulas on this page
\[ 153 = 3^{2} \times 17 \]153 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 6 |
| Sum of divisors | 234 |
| Euler totient φ(n) | 96 |
| Square | 23409 |
| Cube | 3581577 |
| Square root | 12.369317 (= 3√17) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 36 |
| Scientific notation | 1.53 × |
153 in other forms
| Form | Value |
|---|---|
| In words | one hundred and fifty-three |
| Roman numerals | CLIII |
| Binary (base 2) | 10011001 |
| Octal (base 8) | 231 |
| Hexadecimal (base 16) | 99 |
| Base 3 | 12200 |
| As time | 153 seconds = 2 min 33 s |
Is 153 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 | Yes (153 ÷ 3 = 51) | 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 3) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 3) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | 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 1) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (153 ÷ 9 = 17) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 3) | 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 9) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 153 a prime number?
No. 153 = × 17, so it is divisible by 3.
What are the factors of 153?
1, 3, 9, 17, 51, 153.
What is 153 in binary?
10011001 (hexadecimal 99, octal 231).
What is the square root of 153?
About 12.3693, exactly 3√17.
What is 153 in Roman numerals?
CLIII.
Is 153 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 153?
153 is an Armstrong number: each digit raised to the power 3 adds up to 153; a triangular number: 1 + 2 + … + 17 = 153; a binary palindrome (10011001); a Harshad number: divisible by its digit sum 9.