The number 46980
46980 is a composite number with 60 divisors. Its prime factorisation is × × 5 × 29. Divisors (60): 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 29, 30, 36 … 46980.
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How to work it out
- 1
What is special about 46980: a Harshad number: divisible by its digit sum 27.
- 2
46980 is composite. Its prime factorisation is
- 3
The divisors add up to 152460; without 46980 itself that is 105480, so 46980 is abundant (105480 is more than 46980). Euler's totient φ(46980) = 12096 numbers up to 46980 share no factor with it.
- 4
The digits of 46980 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
\[ 46980 = 2^{2} \times 3^{4} \times 5 \times 29 \]46980 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 60 |
| Sum of divisors | 152460 |
| Euler totient φ(n) | 12096 |
| Square | 2207120400 |
| Cube | 103690516392000 |
| Square root | 216.748702 (= 18√145) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 83 |
| Scientific notation | 4.698 × |
46980 in other forms
| Form | Value |
|---|---|
| In words | forty-six thousand nine hundred and eighty |
| Binary (base 2) | 1011011110000100 |
| Octal (base 8) | 133604 |
| Hexadecimal (base 16) | B784 |
| Base 3 | 2101110000 |
| As time | 46980 seconds = 13 h 3 min 0 s |
Is 46980 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (46980 ÷ 2 = 23490) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (46980 ÷ 3 = 15660) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (46980 ÷ 4 = 11745) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (46980 ÷ 5 = 9396) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (46980 ÷ 6 = 7830) | 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 (46980 ÷ 9 = 5220) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (46980 ÷ 10 = 4698) | 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 (46980 ÷ 12 = 3915) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 46980 a prime number?
No. 46980 = × × 5 × 29, so it is divisible by 2.
What are the factors of 46980?
1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 29, 30, 36, 45, 54, 58, 60, 81, 87, 90, 108, 116, 135, 145, 162, 174, 180, 261, 270, 290, 324, 348, 405, 435, 522, 540, 580, 783, 810, 870, 1044, 1305, 1566, 1620, 1740, 2349, 2610, 3132, 3915, 4698, 5220, 7830, 9396, 11745, 15660, 23490, 46980.
What is 46980 in binary?
1011011110000100 (hexadecimal B784, octal 133604).
What is the square root of 46980?
About 216.7487, exactly 18√145.
Is 46980 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 46980?
46980 is a Harshad number: divisible by its digit sum 27.