The number 83664

Q: Is 83664 a prime number?

No. 83664 = 2^4 × 3^2 × 7 × 83, so it is divisible by 2.

83664 is a composite number with 60 divisors. Its prime factorisation is $2^{4}$ × $3^{2}$ × 7 × 83. Divisors (60): 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 36 … 83664.

Number

Pick any whole number from 1 to 100,000.

83664 = 2^{4} \times 3^{2} \times 7 \times 83

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How to work it out

1
83664 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
2
83664 is composite. Its prime factorisation is
$83664 = 2^{4} \times 3^{2} \times 7 \times 83$
3
The divisors add up to 270816; without 83664 itself that is 187152, so 83664 is abundant (187152 is more than 83664). Euler's totient φ(83664) = 23616 numbers up to 83664 share no factor with it.
4
The digits of 83664 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 182 steps to reach 1.

LaTeX source of the formulas on this page

\[ 83664 = 2^{4} \times 3^{2} \times 7 \times 83 \]

83664 at a glance

Property	Value
Type	composite
Number of divisors	60
Sum of divisors	270816
Euler totient φ(n)	23616
Square	6999664896
Cube	585619963858944
Square root	289.247299 (= 12√581)
Digit sum / digital root	27 / 9
Collatz steps to 1	182
Scientific notation	8.3664 × $10^{4}$

83664 in other forms

Form	Value
In words	eighty-three thousand six hundred and sixty-four
Binary (base 2)	10100011011010000
Octal (base 8)	243320
Hexadecimal (base 16)	146D0
Base 3	11020202200
As time	83664 seconds = 23 h 14 min 24 s

Is 83664 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (83664 ÷ 2 = 41832)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (83664 ÷ 3 = 27888)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (83664 ÷ 4 = 20916)	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 (83664 ÷ 6 = 13944)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	Yes (83664 ÷ 7 = 11952)	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	Yes (83664 ÷ 8 = 10458)	A number is divisible by 8 if the last three digits make a multiple of 8.
9	Yes (83664 ÷ 9 = 9296)	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	No (remainder 9)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (83664 ÷ 12 = 6972)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 83664 a prime number?

No. 83664 = $2^{4}$ × $3^{2}$ × 7 × 83, so it is divisible by 2.

What are the factors of 83664?

1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 36, 42, 48, 56, 63, 72, 83, 84, 112, 126, 144, 166, 168, 249, 252, 332, 336, 498, 504, 581, 664, 747, 996, 1008, 1162, 1328, 1494, 1743, 1992, 2324, 2988, 3486, 3984, 4648, 5229, 5976, 6972, 9296, 10458, 11952, 13944, 20916, 27888, 41832, 83664.

What is 83664 in binary?

10100011011010000 (hexadecimal 146D0, octal 243320).

What is the square root of 83664?

About 289.2473, exactly 12√581.

Is 83664 divisible by 3?

Yes. Its digits add up to 27, a multiple of 3.

What is special about the number 83664?

It is a composite number with 60 divisors.