The number 67872
67872 is a composite number with 48 divisors. Its prime factorisation is × 3 × 7 × 101. Divisors (48): 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48 … 67872.
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How to work it out
- 1
67872 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
67872 is composite. Its prime factorisation is
- 3
The divisors add up to 205632; without 67872 itself that is 137760, so 67872 is abundant (137760 is more than 67872). Euler's totient φ(67872) = 19200 numbers up to 67872 share no factor with it.
- 4
The digits of 67872 add up to 30, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 112 steps to reach 1.
LaTeX source of the formulas on this page
\[ 67872 = 2^{5} \times 3 \times 7 \times 101 \]67872 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 205632 |
| Euler totient φ(n) | 19200 |
| Square | 4606608384 |
| Cube | 312659724238848 |
| Square root | 260.522552 (= 4√4242) |
| Digit sum / digital root | 30 / 3 |
| Collatz steps to 1 | 112 |
| Scientific notation | 6.7872 × |
67872 in other forms
| Form | Value |
|---|---|
| In words | sixty-seven thousand eight hundred and seventy-two |
| Binary (base 2) | 10000100100100000 |
| Octal (base 8) | 204440 |
| Hexadecimal (base 16) | 10920 |
| Base 3 | 10110002210 |
| As time | 67872 seconds = 18 h 51 min 12 s |
Is 67872 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (67872 ÷ 2 = 33936) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (67872 ÷ 3 = 22624) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (67872 ÷ 4 = 16968) | 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 (67872 ÷ 6 = 11312) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (67872 ÷ 7 = 9696) | 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 (67872 ÷ 8 = 8484) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | 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 2) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (67872 ÷ 12 = 5656) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 67872 a prime number?
No. 67872 = × 3 × 7 × 101, so it is divisible by 2.
What are the factors of 67872?
1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48, 56, 84, 96, 101, 112, 168, 202, 224, 303, 336, 404, 606, 672, 707, 808, 1212, 1414, 1616, 2121, 2424, 2828, 3232, 4242, 4848, 5656, 8484, 9696, 11312, 16968, 22624, 33936, 67872.
What is 67872 in binary?
10000100100100000 (hexadecimal 10920, octal 204440).
What is the square root of 67872?
About 260.5226, exactly 4√4242.
Is 67872 divisible by 3?
Yes. Its digits add up to 30, a multiple of 3.
What is special about the number 67872?
It is a composite number with 48 divisors.