The number 32742
32742 is a composite number with 24 divisors. Its prime factorisation is 2 × × 17 × 107. Divisors (24): 1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 107, 153, 214, 306, 321, 642 … 32742.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 32742: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.
- 2
32742 is composite. Its prime factorisation is
- 3
The divisors add up to 75816; without 32742 itself that is 43074, so 32742 is abundant (43074 is more than 32742). Euler's totient φ(32742) = 10176 numbers up to 32742 share no factor with it.
- 4
The digits of 32742 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 129 steps to reach 1.
LaTeX source of the formulas on this page
\[ 32742 = 2 \times 3^{2} \times 17 \times 107 \]32742 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 75816 |
| Euler totient φ(n) | 10176 |
| Square | 1072038564 |
| Cube | 35100686662488 |
| Square root | 180.947506 (= 3√3638) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 129 |
| Scientific notation | 3.2742 × |
32742 in other forms
| Form | Value |
|---|---|
| In words | thirty-two thousand seven hundred and forty-two |
| Binary (base 2) | 111111111100110 |
| Octal (base 8) | 77746 |
| Hexadecimal (base 16) | 7FE6 |
| Base 3 | 1122220200 |
| As time | 32742 seconds = 9 h 5 min 42 s |
Is 32742 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (32742 ÷ 2 = 16371) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (32742 ÷ 3 = 10914) | 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 2) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (32742 ÷ 6 = 5457) | 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 6) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (32742 ÷ 9 = 3638) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 2) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 6) | 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 32742 a prime number?
No. 32742 = 2 × × 17 × 107, so it is divisible by 2.
What are the factors of 32742?
1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 107, 153, 214, 306, 321, 642, 963, 1819, 1926, 3638, 5457, 10914, 16371, 32742.
What is 32742 in binary?
111111111100110 (hexadecimal 7FE6, octal 77746).
What is the square root of 32742?
About 180.9475, exactly 3√3638.
Is 32742 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 32742?
32742 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.