The number 46971
46971 is a triangular number: 1 + 2 + … + 306 = 46971. Its prime factorisation is × 17 × 307. Divisors (12): 1, 3, 9, 17, 51, 153, 307, 921, 2763, 5219, 15657, 46971.
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How to work it out
- 1
What is special about 46971: a triangular number: 1 + 2 + … + 306 = 46971.
- 2
46971 is composite. Its prime factorisation is
- 3
The divisors add up to 72072; without 46971 itself that is 25101, so 46971 is deficient (25101 is less than 46971). Euler's totient φ(46971) = 29376 numbers up to 46971 share no factor with it.
- 4
The digits of 46971 add up to 27, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 83 steps to reach 1.
LaTeX source of the formulas on this page
\[ 46971 = 3^{2} \times 17 \times 307 \]46971 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 72072 |
| Euler totient φ(n) | 29376 |
| Square | 2206274841 |
| Cube | 103630935556611 |
| Square root | 216.727940 (= 3√5219) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 83 |
| Scientific notation | 4.6971 × |
46971 in other forms
| Form | Value |
|---|---|
| In words | forty-six thousand nine hundred and seventy-one |
| Binary (base 2) | 1011011101111011 |
| Octal (base 8) | 133573 |
| Hexadecimal (base 16) | B77B |
| Base 3 | 2101102200 |
| As time | 46971 seconds = 13 h 2 min 51 s |
Is 46971 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | No (remainder 1) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (46971 ÷ 3 = 15657) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 3) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 1) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 3) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 1) | 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 3) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (46971 ÷ 9 = 5219) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 1) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 3) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 46971 a prime number?
No. 46971 = × 17 × 307, so it is divisible by 3.
What are the factors of 46971?
1, 3, 9, 17, 51, 153, 307, 921, 2763, 5219, 15657, 46971.
What is 46971 in binary?
1011011101111011 (hexadecimal B77B, octal 133573).
What is the square root of 46971?
About 216.7279, exactly 3√5219.
Is 46971 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 46971?
46971 is a triangular number: 1 + 2 + … + 306 = 46971.