The number 32340

Q: Is 32340 a prime number?

No. 32340 = 2^2 × 3 × 5 × 7^2 × 11, so it is divisible by 2.

32340 is a composite number with 72 divisors. Its prime factorisation is $2^{2}$ × 3 × 5 × $7^{2}$ × 11. Divisors (72): 1, 2, 3, 4, 5, 6, 7, 10, 11, 12, 14, 15, 20, 21, 22, 28 … 32340.

Number

Pick any whole number from 1 to 100,000.

32340 = 2^{2} \times 3 \times 5 \times 7^{2} \times 11

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How to work it out

1
What is special about 32340: a Harshad number: divisible by its digit sum 12.
2
32340 is composite. Its prime factorisation is
$32340 = 2^{2} \times 3 \times 5 \times 7^{2} \times 11$
3
The divisors add up to 114912; without 32340 itself that is 82572, so 32340 is abundant (82572 is more than 32340). Euler's totient φ(32340) = 6720 numbers up to 32340 share no factor with it.
4
The digits of 32340 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 67 steps to reach 1.

LaTeX source of the formulas on this page

\[ 32340 = 2^{2} \times 3 \times 5 \times 7^{2} \times 11 \]

32340 at a glance

Property	Value
Type	composite
Number of divisors	72
Sum of divisors	114912
Euler totient φ(n)	6720
Square	1045875600
Cube	33823616904000
Square root	179.833256 (= 14√165)
Digit sum / digital root	12 / 3
Collatz steps to 1	67
Scientific notation	3.234 × $10^{4}$

32340 in other forms

Form	Value
In words	thirty-two thousand three hundred and forty
Binary (base 2)	111111001010100
Octal (base 8)	77124
Hexadecimal (base 16)	7E54
Base 3	1122100210
As time	32340 seconds = 8 h 59 min 0 s

Is 32340 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (32340 ÷ 2 = 16170)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (32340 ÷ 3 = 10780)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (32340 ÷ 4 = 8085)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (32340 ÷ 5 = 6468)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (32340 ÷ 6 = 5390)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	Yes (32340 ÷ 7 = 4620)	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	No (remainder 4)	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 (32340 ÷ 10 = 3234)	A number is divisible by 10 if the last digit is 0.
11	Yes (32340 ÷ 11 = 2940)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (32340 ÷ 12 = 2695)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 32340 a prime number?

No. 32340 = $2^{2}$ × 3 × 5 × $7^{2}$ × 11, so it is divisible by 2.

What are the factors of 32340?

1, 2, 3, 4, 5, 6, 7, 10, 11, 12, 14, 15, 20, 21, 22, 28, 30, 33, 35, 42, 44, 49, 55, 60, 66, 70, 77, 84, 98, 105, 110, 132, 140, 147, 154, 165, 196, 210, 220, 231, 245, 294, 308, 330, 385, 420, 462, 490, 539, 588, 660, 735, 770, 924, 980, 1078, 1155, 1470, 1540, 1617, 2156, 2310, 2695, 2940, 3234, 4620, 5390, 6468, 8085, 10780, 16170, 32340.

What is 32340 in binary?

111111001010100 (hexadecimal 7E54, octal 77124).

What is the square root of 32340?

About 179.8333, exactly 14√165.

Is 32340 divisible by 3?

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

What is special about the number 32340?

32340 is a Harshad number: divisible by its digit sum 12.