The number 72168
72168 is a composite number with 32 divisors. Its prime factorisation is × 3 × 31 × 97. Divisors (32): 1, 2, 3, 4, 6, 8, 12, 24, 31, 62, 93, 97, 124, 186, 194, 248 … 72168.
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How to work it out
- 1
What is special about 72168: a Harshad number: divisible by its digit sum 24.
- 2
72168 is composite. Its prime factorisation is
- 3
The divisors add up to 188160; without 72168 itself that is 115992, so 72168 is abundant (115992 is more than 72168). Euler's totient φ(72168) = 23040 numbers up to 72168 share no factor with it.
- 4
The digits of 72168 add up to 24, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 143 steps to reach 1.
LaTeX source of the formulas on this page
\[ 72168 = 2^{3} \times 3 \times 31 \times 97 \]72168 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 188160 |
| Euler totient φ(n) | 23040 |
| Square | 5208220224 |
| Cube | 375866837125632 |
| Square root | 268.641024 (= 2√18042) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 143 |
| Scientific notation | 7.2168 × |
72168 in other forms
| Form | Value |
|---|---|
| In words | seventy-two thousand one hundred and sixty-eight |
| Binary (base 2) | 10001100111101000 |
| Octal (base 8) | 214750 |
| Hexadecimal (base 16) | 119E8 |
| Base 3 | 10122222220 |
| As time | 72168 seconds = 20 h 2 min 48 s |
Is 72168 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (72168 ÷ 2 = 36084) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (72168 ÷ 3 = 24056) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (72168 ÷ 4 = 18042) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 3) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (72168 ÷ 6 = 12028) | 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 | Yes (72168 ÷ 8 = 9021) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 8) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 8) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (72168 ÷ 12 = 6014) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 72168 a prime number?
No. 72168 = × 3 × 31 × 97, so it is divisible by 2.
What are the factors of 72168?
1, 2, 3, 4, 6, 8, 12, 24, 31, 62, 93, 97, 124, 186, 194, 248, 291, 372, 388, 582, 744, 776, 1164, 2328, 3007, 6014, 9021, 12028, 18042, 24056, 36084, 72168.
What is 72168 in binary?
10001100111101000 (hexadecimal 119E8, octal 214750).
What is the square root of 72168?
About 268.6410, exactly 2√18042.
Is 72168 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 72168?
72168 is a Harshad number: divisible by its digit sum 24.