The number 34848

Q: Is 34848 a prime number?

No. 34848 = 2^5 × 3^2 × 11^2, so it is divisible by 2.

34848 is a composite number with 54 divisors. Its prime factorisation is $2^{5}$ × $3^{2}$ × $11^{2}$ . Divisors (54): 1, 2, 3, 4, 6, 8, 9, 11, 12, 16, 18, 22, 24, 32, 33, 36 … 34848.

Number

Pick any whole number from 1 to 100,000.

34848 = 2^{5} \times 3^{2} \times 11^{2}

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How to work it out

1
34848 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
2
34848 is composite. Its prime factorisation is
$34848 = 2^{5} \times 3^{2} \times 11^{2}$
3
The divisors add up to 108927; without 34848 itself that is 74079, so 34848 is abundant (74079 is more than 34848). Euler's totient φ(34848) = 10560 numbers up to 34848 share no factor with it.
4
The digits of 34848 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 49 steps to reach 1.

LaTeX source of the formulas on this page

\[ 34848 = 2^{5} \times 3^{2} \times 11^{2} \]

34848 at a glance

Property	Value
Type	composite
Number of divisors	54
Sum of divisors	108927
Euler totient φ(n)	10560
Square	1214383104
Cube	42318822408192
Square root	186.676190 (= 132√2)
Digit sum / digital root	27 / 9
Collatz steps to 1	49
Scientific notation	3.4848 × $10^{4}$

34848 in other forms

Form	Value
In words	thirty-four thousand eight hundred and forty-eight
Binary (base 2)	1000100000100000
Octal (base 8)	104040
Hexadecimal (base 16)	8820
Base 3	1202210200
As time	34848 seconds = 9 h 40 min 48 s

Is 34848 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (34848 ÷ 2 = 17424)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (34848 ÷ 3 = 11616)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (34848 ÷ 4 = 8712)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	No (remainder 3)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (34848 ÷ 6 = 5808)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	No (remainder 2)	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 (34848 ÷ 8 = 4356)	A number is divisible by 8 if the last three digits make a multiple of 8.
9	Yes (34848 ÷ 9 = 3872)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	No (remainder 8)	A number is divisible by 10 if the last digit is 0.
11	Yes (34848 ÷ 11 = 3168)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (34848 ÷ 12 = 2904)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 34848 a prime number?

No. 34848 = $2^{5}$ × $3^{2}$ × $11^{2}$ , so it is divisible by 2.

What are the factors of 34848?

1, 2, 3, 4, 6, 8, 9, 11, 12, 16, 18, 22, 24, 32, 33, 36, 44, 48, 66, 72, 88, 96, 99, 121, 132, 144, 176, 198, 242, 264, 288, 352, 363, 396, 484, 528, 726, 792, 968, 1056, 1089, 1452, 1584, 1936, 2178, 2904, 3168, 3872, 4356, 5808, 8712, 11616, 17424, 34848.

What is 34848 in binary?

1000100000100000 (hexadecimal 8820, octal 104040).

What is the square root of 34848?

About 186.6762, exactly 132√2.

Is 34848 divisible by 3?

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

What is special about the number 34848?

It is a composite number with 54 divisors.