The number 84084

Q: Is 84084 a prime number?

No. 84084 = 2^2 × 3 × 7^2 × 11 × 13, so it is divisible by 2.

84084 is a composite number with 72 divisors. Its prime factorisation is $2^{2}$ × 3 × $7^{2}$ × 11 × 13. Divisors (72): 1, 2, 3, 4, 6, 7, 11, 12, 13, 14, 21, 22, 26, 28, 33, 39 … 84084.

Number

Pick any whole number from 1 to 100,000.

84084 = 2^{2} \times 3 \times 7^{2} \times 11 \times 13

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How to work it out

1
84084 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
2
84084 is composite. Its prime factorisation is
$84084 = 2^{2} \times 3 \times 7^{2} \times 11 \times 13$
3
The divisors add up to 268128; without 84084 itself that is 184044, so 84084 is abundant (184044 is more than 84084). Euler's totient φ(84084) = 20160 numbers up to 84084 share no factor with it.
4
The digits of 84084 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 89 steps to reach 1.

LaTeX source of the formulas on this page

\[ 84084 = 2^{2} \times 3 \times 7^{2} \times 11 \times 13 \]

84084 at a glance

Property	Value
Type	composite
Number of divisors	72
Sum of divisors	268128
Euler totient φ(n)	20160
Square	7070119056
Cube	594483890704704
Square root	289.972412 (= 14√429)
Digit sum / digital root	24 / 6
Collatz steps to 1	89
Scientific notation	8.4084 × $10^{4}$

84084 in other forms

Form	Value
In words	eighty-four thousand and eighty-four
Binary (base 2)	10100100001110100
Octal (base 8)	244164
Hexadecimal (base 16)	14874
Base 3	11021100020
As time	84084 seconds = 23 h 21 min 24 s

Is 84084 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (84084 ÷ 2 = 42042)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (84084 ÷ 3 = 28028)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (84084 ÷ 4 = 21021)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	No (remainder 4)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (84084 ÷ 6 = 14014)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	Yes (84084 ÷ 7 = 12012)	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 6)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	No (remainder 4)	A number is divisible by 10 if the last digit is 0.
11	Yes (84084 ÷ 11 = 7644)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (84084 ÷ 12 = 7007)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 84084 a prime number?

No. 84084 = $2^{2}$ × 3 × $7^{2}$ × 11 × 13, so it is divisible by 2.

What are the factors of 84084?

1, 2, 3, 4, 6, 7, 11, 12, 13, 14, 21, 22, 26, 28, 33, 39, 42, 44, 49, 52, 66, 77, 78, 84, 91, 98, 132, 143, 147, 154, 156, 182, 196, 231, 273, 286, 294, 308, 364, 429, 462, 539, 546, 572, 588, 637, 858, 924, 1001, 1078, 1092, 1274, 1617, 1716, 1911, 2002, 2156, 2548, 3003, 3234, 3822, 4004, 6006, 6468, 7007, 7644, 12012, 14014, 21021, 28028, 42042, 84084.

What is 84084 in binary?

10100100001110100 (hexadecimal 14874, octal 244164).

What is the square root of 84084?

About 289.9724, exactly 14√429.

Is 84084 divisible by 3?

Yes. Its digits add up to 24, a multiple of 3.

What is special about the number 84084?

It is a composite number with 72 divisors.