The number 144
144 is a Fibonacci number and a perfect square (12²). Its prime factorisation is × . Divisors (15): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 144: a Fibonacci number; a perfect square (12²); a Harshad number: divisible by its digit sum 9.
- 2
144 is composite. Its prime factorisation is
- 3
The divisors add up to 403; without 144 itself that is 259, so 144 is abundant (259 is more than 144). Euler's totient φ(144) = 48 numbers up to 144 share no factor with it.
- 4
The digits of 144 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 23 steps to reach 1.
LaTeX source of the formulas on this page
\[ 144 = 2^{4} \times 3^{2} \]144 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 15 |
| Sum of divisors | 403 |
| Euler totient φ(n) | 48 |
| Square | 20736 |
| Cube | 2985984 |
| Square root | 12 |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 23 |
| Scientific notation | 1.44 × |
| Perfect power |
144 in other forms
| Form | Value |
|---|---|
| In words | one hundred and forty-four |
| Roman numerals | CXLIV |
| Binary (base 2) | 10010000 |
| Octal (base 8) | 220 |
| Hexadecimal (base 16) | 90 |
| Base 3 | 12100 |
| As time | 144 seconds = 2 min 24 s |
Is 144 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (144 ÷ 2 = 72) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (144 ÷ 3 = 48) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (144 ÷ 4 = 36) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 4) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (144 ÷ 6 = 24) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 (144 ÷ 8 = 18) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (144 ÷ 9 = 16) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 4) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (144 ÷ 12 = 12) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 144 a prime number?
No. 144 = × , so it is divisible by 2.
What are the factors of 144?
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144.
What is 144 in binary?
10010000 (hexadecimal 90, octal 220).
What is the square root of 144?
12, because 12 × 12 = 144.
What is 144 in Roman numerals?
CXLIV.
Is 144 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 144?
144 is a Fibonacci number; a perfect square (12²); a Harshad number: divisible by its digit sum 9.