The number 126
126 is a composite number with 12 divisors. Its prime factorisation is 2 × × 7. Divisors (12): 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 126: a Harshad number: divisible by its digit sum 9.
- 2
126 is composite. Its prime factorisation is
- 3
The divisors add up to 312; without 126 itself that is 186, so 126 is abundant (186 is more than 126). Euler's totient φ(126) = 36 numbers up to 126 share no factor with it.
- 4
The digits of 126 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 108 steps to reach 1.
LaTeX source of the formulas on this page
\[ 126 = 2 \times 3^{2} \times 7 \]126 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 312 |
| Euler totient φ(n) | 36 |
| Square | 15876 |
| Cube | 2000376 |
| Square root | 11.224972 (= 3√14) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 108 |
| Scientific notation | 1.26 × |
126 in other forms
| Form | Value |
|---|---|
| In words | one hundred and twenty-six |
| Roman numerals | CXXVI |
| Binary (base 2) | 1111110 |
| Octal (base 8) | 176 |
| Hexadecimal (base 16) | 7E |
| Base 3 | 11200 |
| As time | 126 seconds = 2 min 6 s |
Is 126 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (126 ÷ 2 = 63) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (126 ÷ 3 = 42) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 2) | 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 | Yes (126 ÷ 6 = 21) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (126 ÷ 7 = 18) | 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 6) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (126 ÷ 9 = 14) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 6) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 5) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 6) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 126 a prime number?
No. 126 = 2 × × 7, so it is divisible by 2.
What are the factors of 126?
1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126.
What is 126 in binary?
1111110 (hexadecimal 7E, octal 176).
What is the square root of 126?
About 11.2250, exactly 3√14.
What is 126 in Roman numerals?
CXXVI.
Is 126 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 126?
126 is a Harshad number: divisible by its digit sum 9.