The number 65340

Q: Is 65340 a prime number?

No. 65340 = 2^2 × 3^3 × 5 × 11^2, so it is divisible by 2.

65340 is a composite number with 72 divisors. Its prime factorisation is $2^{2}$ × $3^{3}$ × 5 × $11^{2}$ . Divisors (72): 1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 15, 18, 20, 22, 27, 30 … 65340.

Number

Pick any whole number from 1 to 100,000.

65340 = 2^{2} \times 3^{3} \times 5 \times 11^{2}

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How to work it out

1
What is special about 65340: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.
2
65340 is composite. Its prime factorisation is
$65340 = 2^{2} \times 3^{3} \times 5 \times 11^{2}$
3
The divisors add up to 223440; without 65340 itself that is 158100, so 65340 is abundant (158100 is more than 65340). Euler's totient φ(65340) = 15840 numbers up to 65340 share no factor with it.
4
The digits of 65340 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 161 steps to reach 1.

LaTeX source of the formulas on this page

\[ 65340 = 2^{2} \times 3^{3} \times 5 \times 11^{2} \]

65340 at a glance

Property	Value
Type	composite
Number of divisors	72
Sum of divisors	223440
Euler totient φ(n)	15840
Square	4269315600
Cube	278957081304000
Square root	255.616901 (= 66√15)
Digit sum / digital root	18 / 9
Collatz steps to 1	161
Scientific notation	6.534 × $10^{4}$

65340 in other forms

Form	Value
In words	sixty-five thousand three hundred and forty
Binary (base 2)	1111111100111100
Octal (base 8)	177474
Hexadecimal (base 16)	FF3C
Base 3	10022122000
As time	65340 seconds = 18 h 9 min 0 s

Is 65340 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (65340 ÷ 2 = 32670)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (65340 ÷ 3 = 21780)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (65340 ÷ 4 = 16335)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (65340 ÷ 5 = 13068)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (65340 ÷ 6 = 10890)	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	No (remainder 4)	A number is divisible by 8 if the last three digits make a multiple of 8.
9	Yes (65340 ÷ 9 = 7260)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (65340 ÷ 10 = 6534)	A number is divisible by 10 if the last digit is 0.
11	Yes (65340 ÷ 11 = 5940)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (65340 ÷ 12 = 5445)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 65340 a prime number?

No. 65340 = $2^{2}$ × $3^{3}$ × 5 × $11^{2}$ , so it is divisible by 2.

What are the factors of 65340?

1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 15, 18, 20, 22, 27, 30, 33, 36, 44, 45, 54, 55, 60, 66, 90, 99, 108, 110, 121, 132, 135, 165, 180, 198, 220, 242, 270, 297, 330, 363, 396, 484, 495, 540, 594, 605, 660, 726, 990, 1089, 1188, 1210, 1452, 1485, 1815, 1980, 2178, 2420, 2970, 3267, 3630, 4356, 5445, 5940, 6534, 7260, 10890, 13068, 16335, 21780, 32670, 65340.

What is 65340 in binary?

1111111100111100 (hexadecimal FF3C, octal 177474).

What is the square root of 65340?

About 255.6169, exactly 66√15.

Is 65340 divisible by 3?

Yes. Its digits add up to 18, a multiple of 3.

What is special about the number 65340?

65340 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.