The number 34272
34272 is a composite number with 72 divisors. Its prime factorisation is × × 7 × 17. Divisors (72): 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 17, 18, 21, 24, 28 … 34272.
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How to work it out
- 1
What is special about 34272: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.
- 2
34272 is composite. Its prime factorisation is
- 3
The divisors add up to 117936; without 34272 itself that is 83664, so 34272 is abundant (83664 is more than 34272). Euler's totient φ(34272) = 9216 numbers up to 34272 share no factor with it.
- 4
The digits of 34272 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 173 steps to reach 1.
LaTeX source of the formulas on this page
\[ 34272 = 2^{5} \times 3^{2} \times 7 \times 17 \]34272 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 72 |
| Sum of divisors | 117936 |
| Euler totient φ(n) | 9216 |
| Square | 1174569984 |
| Cube | 40254862491648 |
| Square root | 185.126983 (= 12√238) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 173 |
| Scientific notation | 3.4272 × |
34272 in other forms
| Form | Value |
|---|---|
| In words | thirty-four thousand two hundred and seventy-two |
| Binary (base 2) | 1000010111100000 |
| Octal (base 8) | 102740 |
| Hexadecimal (base 16) | 85E0 |
| Base 3 | 1202000100 |
| As time | 34272 seconds = 9 h 31 min 12 s |
Is 34272 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (34272 ÷ 2 = 17136) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (34272 ÷ 3 = 11424) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (34272 ÷ 4 = 8568) | 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 (34272 ÷ 6 = 5712) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (34272 ÷ 7 = 4896) | 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 (34272 ÷ 8 = 4284) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (34272 ÷ 9 = 3808) | 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 7) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (34272 ÷ 12 = 2856) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 34272 a prime number?
No. 34272 = × × 7 × 17, so it is divisible by 2.
What are the factors of 34272?
1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 17, 18, 21, 24, 28, 32, 34, 36, 42, 48, 51, 56, 63, 68, 72, 84, 96, 102, 112, 119, 126, 136, 144, 153, 168, 204, 224, 238, 252, 272, 288, 306, 336, 357, 408, 476, 504, 544, 612, 672, 714, 816, 952, 1008, 1071, 1224, 1428, 1632, 1904, 2016, 2142, 2448, 2856, 3808, 4284, 4896, 5712, 8568, 11424, 17136, 34272.
What is 34272 in binary?
1000010111100000 (hexadecimal 85E0, octal 102740).
What is the square root of 34272?
About 185.1270, exactly 12√238.
Is 34272 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 34272?
34272 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.