The number 84180

Q: Is 84180 a prime number?

No. 84180 = 2^2 × 3 × 5 × 23 × 61, so it is divisible by 2.

84180 is a composite number with 48 divisors. Its prime factorisation is $2^{2}$ × 3 × 5 × 23 × 61. Divisors (48): 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 23, 30, 46, 60, 61, 69 … 84180.

Number

Pick any whole number from 1 to 100,000.

84180 = 2^{2} \times 3 \times 5 \times 23 \times 61

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How to work it out

1
84180 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
2
84180 is composite. Its prime factorisation is
$84180 = 2^{2} \times 3 \times 5 \times 23 \times 61$
3
The divisors add up to 249984; without 84180 itself that is 165804, so 84180 is abundant (165804 is more than 84180). Euler's totient φ(84180) = 21120 numbers up to 84180 share no factor with it.
4
The digits of 84180 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 58 steps to reach 1.

LaTeX source of the formulas on this page

\[ 84180 = 2^{2} \times 3 \times 5 \times 23 \times 61 \]

84180 at a glance

Property	Value
Type	composite
Number of divisors	48
Sum of divisors	249984
Euler totient φ(n)	21120
Square	7086272400
Cube	596522410632000
Square root	290.137898 (= 2√21045)
Digit sum / digital root	21 / 3
Collatz steps to 1	58
Scientific notation	8.418 × $10^{4}$

84180 in other forms

Form	Value
In words	eighty-four thousand one hundred and eighty
Binary (base 2)	10100100011010100
Octal (base 8)	244324
Hexadecimal (base 16)	148D4
Base 3	11021110210
As time	84180 seconds = 23 h 23 min 0 s

Is 84180 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (84180 ÷ 2 = 42090)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (84180 ÷ 3 = 28060)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (84180 ÷ 4 = 21045)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (84180 ÷ 5 = 16836)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (84180 ÷ 6 = 14030)	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	No (remainder 4)	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	Yes (84180 ÷ 10 = 8418)	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 (84180 ÷ 12 = 7015)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 84180 a prime number?

No. 84180 = $2^{2}$ × 3 × 5 × 23 × 61, so it is divisible by 2.

What are the factors of 84180?

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 23, 30, 46, 60, 61, 69, 92, 115, 122, 138, 183, 230, 244, 276, 305, 345, 366, 460, 610, 690, 732, 915, 1220, 1380, 1403, 1830, 2806, 3660, 4209, 5612, 7015, 8418, 14030, 16836, 21045, 28060, 42090, 84180.

What is 84180 in binary?

10100100011010100 (hexadecimal 148D4, octal 244324).

What is the square root of 84180?

About 290.1379, exactly 2√21045.

Is 84180 divisible by 3?

Yes. Its digits add up to 21, a multiple of 3.

What is special about the number 84180?

It is a composite number with 48 divisors.