The number 71872
71872 is a composite number with 14 divisors. Its prime factorisation is × 1123. Divisors (14): 1, 2, 4, 8, 16, 32, 64, 1123, 2246, 4492, 8984, 17968, 35936, 71872.
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How to work it out
- 1
What is special about 71872: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
71872 is composite. Its prime factorisation is
- 3
The divisors add up to 142748; without 71872 itself that is 70876, so 71872 is deficient (70876 is less than 71872). Euler's totient φ(71872) = 35904 numbers up to 71872 share no factor with it.
- 4
The digits of 71872 add up to 25, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 50 steps to reach 1.
LaTeX source of the formulas on this page
\[ 71872 = 2^{6} \times 1123 \]71872 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 14 |
| Sum of divisors | 142748 |
| Euler totient φ(n) | 35904 |
| Square | 5165584384 |
| Cube | 371260880846848 |
| Square root | 268.089537 (= 8√1123) |
| Digit sum / digital root | 25 / 7 |
| Collatz steps to 1 | 50 |
| Scientific notation | 7.1872 × |
71872 in other forms
| Form | Value |
|---|---|
| In words | seventy-one thousand eight hundred and seventy-two |
| Binary (base 2) | 10001100011000000 |
| Octal (base 8) | 214300 |
| Hexadecimal (base 16) | 118C0 |
| Base 3 | 10122120221 |
| As time | 71872 seconds = 19 h 57 min 52 s |
Is 71872 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (71872 ÷ 2 = 35936) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (71872 ÷ 4 = 17968) | 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 | No (remainder 4) | 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 | Yes (71872 ÷ 8 = 8984) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 7) | 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 9) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 71872 a prime number?
No. 71872 = × 1123, so it is divisible by 2.
What are the factors of 71872?
1, 2, 4, 8, 16, 32, 64, 1123, 2246, 4492, 8984, 17968, 35936, 71872.
What is 71872 in binary?
10001100011000000 (hexadecimal 118C0, octal 214300).
What is the square root of 71872?
About 268.0895, exactly 8√1123.
Is 71872 divisible by 3?
No. Its digits add up to 25, which is not a multiple of 3.
What is special about the number 71872?
71872 is a happy number: repeatedly adding the squares of its digits reaches 1.