The number 83952

Q: Is 83952 a prime number?

No. 83952 = 2^4 × 3^2 × 11 × 53, so it is divisible by 2.

83952 is a composite number with 60 divisors. Its prime factorisation is $2^{4}$ × $3^{2}$ × 11 × 53. Divisors (60): 1, 2, 3, 4, 6, 8, 9, 11, 12, 16, 18, 22, 24, 33, 36, 44 … 83952.

Number

Pick any whole number from 1 to 100,000.

83952 = 2^{4} \times 3^{2} \times 11 \times 53

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How to work it out

1
83952 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
2
83952 is composite. Its prime factorisation is
$83952 = 2^{4} \times 3^{2} \times 11 \times 53$
3
The divisors add up to 261144; without 83952 itself that is 177192, so 83952 is abundant (177192 is more than 83952). Euler's totient φ(83952) = 24960 numbers up to 83952 share no factor with it.
4
The digits of 83952 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 89 steps to reach 1.

LaTeX source of the formulas on this page

\[ 83952 = 2^{4} \times 3^{2} \times 11 \times 53 \]

83952 at a glance

Property	Value
Type	composite
Number of divisors	60
Sum of divisors	261144
Euler totient φ(n)	24960
Square	7047938304
Cube	591688516497408
Square root	289.744715 (= 12√583)
Digit sum / digital root	27 / 9
Collatz steps to 1	89
Scientific notation	8.3952 × $10^{4}$

83952 in other forms

Form	Value
In words	eighty-three thousand nine hundred and fifty-two
Binary (base 2)	10100011111110000
Octal (base 8)	243760
Hexadecimal (base 16)	147F0
Base 3	11021011100
As time	83952 seconds = 23 h 19 min 12 s

Is 83952 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (83952 ÷ 2 = 41976)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (83952 ÷ 3 = 27984)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (83952 ÷ 4 = 20988)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	No (remainder 2)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (83952 ÷ 6 = 13992)	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	Yes (83952 ÷ 8 = 10494)	A number is divisible by 8 if the last three digits make a multiple of 8.
9	Yes (83952 ÷ 9 = 9328)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	No (remainder 2)	A number is divisible by 10 if the last digit is 0.
11	Yes (83952 ÷ 11 = 7632)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (83952 ÷ 12 = 6996)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 83952 a prime number?

No. 83952 = $2^{4}$ × $3^{2}$ × 11 × 53, so it is divisible by 2.

What are the factors of 83952?

1, 2, 3, 4, 6, 8, 9, 11, 12, 16, 18, 22, 24, 33, 36, 44, 48, 53, 66, 72, 88, 99, 106, 132, 144, 159, 176, 198, 212, 264, 318, 396, 424, 477, 528, 583, 636, 792, 848, 954, 1166, 1272, 1584, 1749, 1908, 2332, 2544, 3498, 3816, 4664, 5247, 6996, 7632, 9328, 10494, 13992, 20988, 27984, 41976, 83952.

What is 83952 in binary?

10100011111110000 (hexadecimal 147F0, octal 243760).

What is the square root of 83952?

About 289.7447, exactly 12√583.

Is 83952 divisible by 3?

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

What is special about the number 83952?

It is a composite number with 60 divisors.