The number 8172
8172 is a composite number with 18 divisors. Its prime factorisation is × × 227. Divisors (18): 1, 2, 3, 4, 6, 9, 12, 18, 36, 227, 454, 681, 908, 1362, 2043, 2724 … 8172.
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How to work it out
- 1
What is special about 8172: a Harshad number: divisible by its digit sum 18.
- 2
8172 is composite. Its prime factorisation is
- 3
The divisors add up to 20748; without 8172 itself that is 12576, so 8172 is abundant (12576 is more than 8172). Euler's totient φ(8172) = 2712 numbers up to 8172 share no factor with it.
- 4
The digits of 8172 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 158 steps to reach 1.
LaTeX source of the formulas on this page
\[ 8172 = 2^{2} \times 3^{2} \times 227 \]8172 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 18 |
| Sum of divisors | 20748 |
| Euler totient φ(n) | 2712 |
| Square | 66781584 |
| Cube | 545739104448 |
| Square root | 90.399115 (= 6√227) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 158 |
| Scientific notation | 8.172 × |
8172 in other forms
| Form | Value |
|---|---|
| In words | eight thousand one hundred and seventy-two |
| Binary (base 2) | 1111111101100 |
| Octal (base 8) | 17754 |
| Hexadecimal (base 16) | 1FEC |
| Base 3 | 102012200 |
| As time | 8172 seconds = 2 h 16 min 12 s |
Is 8172 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (8172 ÷ 2 = 4086) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (8172 ÷ 3 = 2724) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (8172 ÷ 4 = 2043) | 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 (8172 ÷ 6 = 1362) | 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 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (8172 ÷ 9 = 908) | 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 10) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (8172 ÷ 12 = 681) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 8172 a prime number?
No. 8172 = × × 227, so it is divisible by 2.
What are the factors of 8172?
1, 2, 3, 4, 6, 9, 12, 18, 36, 227, 454, 681, 908, 1362, 2043, 2724, 4086, 8172.
What is 8172 in binary?
1111111101100 (hexadecimal 1FEC, octal 17754).
What is the square root of 8172?
About 90.3991, exactly 6√227.
Is 8172 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 8172?
8172 is a Harshad number: divisible by its digit sum 18.