The number 72126
72126 is a composite number with 12 divisors. Its prime factorisation is 2 × × 4007. Divisors (12): 1, 2, 3, 6, 9, 18, 4007, 8014, 12021, 24042, 36063, 72126.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 72126: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.
- 2
72126 is composite. Its prime factorisation is
- 3
The divisors add up to 156312; without 72126 itself that is 84186, so 72126 is abundant (84186 is more than 72126). Euler's totient φ(72126) = 24036 numbers up to 72126 share no factor with it.
- 4
The digits of 72126 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 94 steps to reach 1.
LaTeX source of the formulas on this page
\[ 72126 = 2 \times 3^{2} \times 4007 \]72126 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 156312 |
| Euler totient φ(n) | 24036 |
| Square | 5202159876 |
| Cube | 375210983216376 |
| Square root | 268.562842 (= 3√8014) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 94 |
| Scientific notation | 7.2126 × |
72126 in other forms
| Form | Value |
|---|---|
| In words | seventy-two thousand one hundred and twenty-six |
| Binary (base 2) | 10001100110111110 |
| Octal (base 8) | 214676 |
| Hexadecimal (base 16) | 119BE |
| Base 3 | 10122221100 |
| As time | 72126 seconds = 20 h 2 min 6 s |
Is 72126 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (72126 ÷ 2 = 36063) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (72126 ÷ 3 = 24042) | 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 (72126 ÷ 6 = 12021) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 (72126 ÷ 9 = 8014) | 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 10) | 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 72126 a prime number?
No. 72126 = 2 × × 4007, so it is divisible by 2.
What are the factors of 72126?
1, 2, 3, 6, 9, 18, 4007, 8014, 12021, 24042, 36063, 72126.
What is 72126 in binary?
10001100110111110 (hexadecimal 119BE, octal 214676).
What is the square root of 72126?
About 268.5628, exactly 3√8014.
Is 72126 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 72126?
72126 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.