The number 97344

Q: Is 97344 a prime number?

No. 97344 = 2^6 × 3^2 × 13^2, so it is divisible by 2.

97344 is a perfect square (312²). Its prime factorisation is $2^{6}$ × $3^{2}$ × $13^{2}$ . Divisors (63): 1, 2, 3, 4, 6, 8, 9, 12, 13, 16, 18, 24, 26, 32, 36, 39 … 97344.

Number

Pick any whole number from 1 to 100,000.

97344 = 2^{6} \times 3^{2} \times 13^{2}

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How to work it out

1
What is special about 97344: a perfect square (312²).
2
97344 is composite. Its prime factorisation is
$97344 = 2^{6} \times 3^{2} \times 13^{2}$
3
The divisors add up to 302133; without 97344 itself that is 204789, so 97344 is abundant (204789 is more than 97344). Euler's totient φ(97344) = 29952 numbers up to 97344 share no factor with it.
4
The digits of 97344 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 115 steps to reach 1.

LaTeX source of the formulas on this page

\[ 97344 = 2^{6} \times 3^{2} \times 13^{2} \]

97344 at a glance

Property	Value
Type	composite
Number of divisors	63
Sum of divisors	302133
Euler totient φ(n)	29952
Square	9475854336
Cube	922417564483584
Square root	312
Digit sum / digital root	27 / 9
Collatz steps to 1	115
Scientific notation	9.7344 × $10^{4}$
Perfect power	$312^{2}$

97344 in other forms

Form	Value
In words	ninety-seven thousand three hundred and forty-four
Binary (base 2)	10111110001000000
Octal (base 8)	276100
Hexadecimal (base 16)	17C40
Base 3	11221112100
As time	97344 seconds = 27 h 2 min 24 s

Is 97344 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (97344 ÷ 2 = 48672)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (97344 ÷ 3 = 32448)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (97344 ÷ 4 = 24336)	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 (97344 ÷ 6 = 16224)	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 (97344 ÷ 8 = 12168)	A number is divisible by 8 if the last three digits make a multiple of 8.
9	Yes (97344 ÷ 9 = 10816)	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 5)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (97344 ÷ 12 = 8112)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 97344 a prime number?

No. 97344 = $2^{6}$ × $3^{2}$ × $13^{2}$ , so it is divisible by 2.

What are the factors of 97344?

1, 2, 3, 4, 6, 8, 9, 12, 13, 16, 18, 24, 26, 32, 36, 39, 48, 52, 64, 72, 78, 96, 104, 117, 144, 156, 169, 192, 208, 234, 288, 312, 338, 416, 468, 507, 576, 624, 676, 832, 936, 1014, 1248, 1352, 1521, 1872, 2028, 2496, 2704, 3042, 3744, 4056, 5408, 6084, 7488, 8112, 10816, 12168, 16224, 24336, 32448, 48672, 97344.

What is 97344 in binary?

10111110001000000 (hexadecimal 17C40, octal 276100).

What is the square root of 97344?

312, because 312 × 312 = 97344.

Is 97344 divisible by 3?

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

What is special about the number 97344?

97344 is a perfect square (312²).