The number 33540

Q: Is 33540 a prime number?

No. 33540 = 2^2 × 3 × 5 × 13 × 43, so it is divisible by 2.

33540 is a composite number with 48 divisors. Its prime factorisation is $2^{2}$ × 3 × 5 × 13 × 43. Divisors (48): 1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 20, 26, 30, 39, 43, 52 … 33540.

Number

Pick any whole number from 1 to 100,000.

33540 = 2^{2} \times 3 \times 5 \times 13 \times 43

Explain it step by step in chat Make a short video of it

How to work it out

1
What is special about 33540: a Harshad number: divisible by its digit sum 15.
2
33540 is composite. Its prime factorisation is
$33540 = 2^{2} \times 3 \times 5 \times 13 \times 43$
3
The divisors add up to 103488; without 33540 itself that is 69948, so 33540 is abundant (69948 is more than 33540). Euler's totient φ(33540) = 8064 numbers up to 33540 share no factor with it.
4
The digits of 33540 add up to 15, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 67 steps to reach 1.

LaTeX source of the formulas on this page

\[ 33540 = 2^{2} \times 3 \times 5 \times 13 \times 43 \]

33540 at a glance

Property	Value
Type	composite
Number of divisors	48
Sum of divisors	103488
Euler totient φ(n)	8064
Square	1124931600
Cube	37730205864000
Square root	183.139291 (= 2√8385)
Digit sum / digital root	15 / 6
Collatz steps to 1	67
Scientific notation	3.354 × $10^{4}$

33540 in other forms

Form	Value
In words	thirty-three thousand five hundred and forty
Binary (base 2)	1000001100000100
Octal (base 8)	101404
Hexadecimal (base 16)	8304
Base 3	1201000020
As time	33540 seconds = 9 h 19 min 0 s

Is 33540 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (33540 ÷ 2 = 16770)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (33540 ÷ 3 = 11180)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (33540 ÷ 4 = 8385)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (33540 ÷ 5 = 6708)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (33540 ÷ 6 = 5590)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	No (remainder 3)	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 6)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (33540 ÷ 10 = 3354)	A number is divisible by 10 if the last digit is 0.
11	No (remainder 1)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (33540 ÷ 12 = 2795)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 33540 a prime number?

No. 33540 = $2^{2}$ × 3 × 5 × 13 × 43, so it is divisible by 2.

What are the factors of 33540?

1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 20, 26, 30, 39, 43, 52, 60, 65, 78, 86, 129, 130, 156, 172, 195, 215, 258, 260, 390, 430, 516, 559, 645, 780, 860, 1118, 1290, 1677, 2236, 2580, 2795, 3354, 5590, 6708, 8385, 11180, 16770, 33540.

What is 33540 in binary?

1000001100000100 (hexadecimal 8304, octal 101404).

What is the square root of 33540?

About 183.1393, exactly 2√8385.

Is 33540 divisible by 3?

Yes. Its digits add up to 15, a multiple of 3.

What is special about the number 33540?

33540 is a Harshad number: divisible by its digit sum 15.