The number 34320

Q: Is 34320 a prime number?

No. 34320 = 2^4 × 3 × 5 × 11 × 13, so it is divisible by 2.

34320 is a composite number with 80 divisors. Its prime factorisation is $2^{4}$ × 3 × 5 × 11 × 13. Divisors (80): 1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 13, 15, 16, 20, 22, 24 … 34320.

Number

Pick any whole number from 1 to 100,000.

34320 = 2^{4} \times 3 \times 5 \times 11 \times 13

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How to work it out

1
What is special about 34320: a Harshad number: divisible by its digit sum 12.
2
34320 is composite. Its prime factorisation is
$34320 = 2^{4} \times 3 \times 5 \times 11 \times 13$
3
The divisors add up to 124992; without 34320 itself that is 90672, so 34320 is abundant (90672 is more than 34320). Euler's totient φ(34320) = 7680 numbers up to 34320 share no factor with it.
4
The digits of 34320 add up to 12, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 80 steps to reach 1.

LaTeX source of the formulas on this page

\[ 34320 = 2^{4} \times 3 \times 5 \times 11 \times 13 \]

34320 at a glance

Property	Value
Type	composite
Number of divisors	80
Sum of divisors	124992
Euler totient φ(n)	7680
Square	1177862400
Cube	40424237568000
Square root	185.256579 (= 4√2145)
Digit sum / digital root	12 / 3
Collatz steps to 1	80
Scientific notation	3.432 × $10^{4}$

34320 in other forms

Form	Value
In words	thirty-four thousand three hundred and twenty
Binary (base 2)	1000011000010000
Octal (base 8)	103020
Hexadecimal (base 16)	8610
Base 3	1202002010
As time	34320 seconds = 9 h 32 min 0 s

Is 34320 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (34320 ÷ 2 = 17160)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (34320 ÷ 3 = 11440)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (34320 ÷ 4 = 8580)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (34320 ÷ 5 = 6864)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (34320 ÷ 6 = 5720)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	No (remainder 6)	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 (34320 ÷ 8 = 4290)	A number is divisible by 8 if the last three digits make a multiple of 8.
9	No (remainder 3)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (34320 ÷ 10 = 3432)	A number is divisible by 10 if the last digit is 0.
11	Yes (34320 ÷ 11 = 3120)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (34320 ÷ 12 = 2860)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 34320 a prime number?

No. 34320 = $2^{4}$ × 3 × 5 × 11 × 13, so it is divisible by 2.

What are the factors of 34320?

1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 13, 15, 16, 20, 22, 24, 26, 30, 33, 39, 40, 44, 48, 52, 55, 60, 65, 66, 78, 80, 88, 104, 110, 120, 130, 132, 143, 156, 165, 176, 195, 208, 220, 240, 260, 264, 286, 312, 330, 390, 429, 440, 520, 528, 572, 624, 660, 715, 780, 858, 880, 1040, 1144, 1320, 1430, 1560, 1716, 2145, 2288, 2640, 2860, 3120, 3432, 4290, 5720, 6864, 8580, 11440, 17160, 34320.

What is 34320 in binary?

1000011000010000 (hexadecimal 8610, octal 103020).

What is the square root of 34320?

About 185.2566, exactly 4√2145.

Is 34320 divisible by 3?

Yes. Its digits add up to 12, a multiple of 3.

What is special about the number 34320?

34320 is a Harshad number: divisible by its digit sum 12.