The number 66000

Q: Is 66000 a prime number?

No. 66000 = 2^4 × 3 × 5^3 × 11, so it is divisible by 2.

66000 is a composite number with 80 divisors. Its prime factorisation is $2^{4}$ × 3 × $5^{3}$ × 11. Divisors (80): 1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 16, 20, 22, 24, 25 … 66000.

Number

Pick any whole number from 1 to 100,000.

66000 = 2^{4} \times 3 \times 5^{3} \times 11

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How to work it out

1
What is special about 66000: a Harshad number: divisible by its digit sum 12.
2
66000 is composite. Its prime factorisation is
$66000 = 2^{4} \times 3 \times 5^{3} \times 11$
3
The divisors add up to 232128; without 66000 itself that is 166128, so 66000 is abundant (166128 is more than 66000). Euler's totient φ(66000) = 16000 numbers up to 66000 share no factor with it.
4
The digits of 66000 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 42 steps to reach 1.

LaTeX source of the formulas on this page

\[ 66000 = 2^{4} \times 3 \times 5^{3} \times 11 \]

66000 at a glance

Property	Value
Type	composite
Number of divisors	80
Sum of divisors	232128
Euler totient φ(n)	16000
Square	4356000000
Cube	287496000000000
Square root	256.904652 (= 20√165)
Digit sum / digital root	12 / 3
Collatz steps to 1	42
Scientific notation	6.6 × $10^{4}$

66000 in other forms

Form	Value
In words	sixty-six thousand
Binary (base 2)	10000000111010000
Octal (base 8)	200720
Hexadecimal (base 16)	101D0
Base 3	10100112110
As time	66000 seconds = 18 h 20 min 0 s

Is 66000 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (66000 ÷ 2 = 33000)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (66000 ÷ 3 = 22000)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (66000 ÷ 4 = 16500)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (66000 ÷ 5 = 13200)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (66000 ÷ 6 = 11000)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	No (remainder 4)	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 (66000 ÷ 8 = 8250)	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 (66000 ÷ 10 = 6600)	A number is divisible by 10 if the last digit is 0.
11	Yes (66000 ÷ 11 = 6000)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (66000 ÷ 12 = 5500)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 66000 a prime number?

No. 66000 = $2^{4}$ × 3 × $5^{3}$ × 11, so it is divisible by 2.

What are the factors of 66000?

1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 16, 20, 22, 24, 25, 30, 33, 40, 44, 48, 50, 55, 60, 66, 75, 80, 88, 100, 110, 120, 125, 132, 150, 165, 176, 200, 220, 240, 250, 264, 275, 300, 330, 375, 400, 440, 500, 528, 550, 600, 660, 750, 825, 880, 1000, 1100, 1200, 1320, 1375, 1500, 1650, 2000, 2200, 2640, 2750, 3000, 3300, 4125, 4400, 5500, 6000, 6600, 8250, 11000, 13200, 16500, 22000, 33000, 66000.

What is 66000 in binary?

10000000111010000 (hexadecimal 101D0, octal 200720).

What is the square root of 66000?

About 256.9047, exactly 20√165.

Is 66000 divisible by 3?

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

What is special about the number 66000?

66000 is a Harshad number: divisible by its digit sum 12.