The number 80730

Q: Is 80730 a prime number?

No. 80730 = 2 × 3^3 × 5 × 13 × 23, so it is divisible by 2.

80730 is a composite number with 64 divisors. Its prime factorisation is 2 × $3^{3}$ × 5 × 13 × 23. Divisors (64): 1, 2, 3, 5, 6, 9, 10, 13, 15, 18, 23, 26, 27, 30, 39, 45 … 80730.

Number

Pick any whole number from 1 to 100,000.

80730 = 2 \times 3^{3} \times 5 \times 13 \times 23

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

How to work it out

1
What is special about 80730: a Harshad number: divisible by its digit sum 18.
2
80730 is composite. Its prime factorisation is
$80730 = 2 \times 3^{3} \times 5 \times 13 \times 23$
3
The divisors add up to 241920; without 80730 itself that is 161190, so 80730 is abundant (161190 is more than 80730). Euler's totient φ(80730) = 19008 numbers up to 80730 share no factor with it.
4
The digits of 80730 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 50 steps to reach 1.

LaTeX source of the formulas on this page

\[ 80730 = 2 \times 3^{3} \times 5 \times 13 \times 23 \]

80730 at a glance

Property	Value
Type	composite
Number of divisors	64
Sum of divisors	241920
Euler totient φ(n)	19008
Square	6517332900
Cube	526144285017000
Square root	284.130252 (= 3√8970)
Digit sum / digital root	18 / 9
Collatz steps to 1	50
Scientific notation	8.073 × $10^{4}$

80730 in other forms

Form	Value
In words	eighty thousand seven hundred and thirty
Binary (base 2)	10011101101011010
Octal (base 8)	235532
Hexadecimal (base 16)	13B5A
Base 3	11002202000
As time	80730 seconds = 22 h 25 min 30 s

Is 80730 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (80730 ÷ 2 = 40365)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (80730 ÷ 3 = 26910)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	No (remainder 2)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (80730 ÷ 5 = 16146)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (80730 ÷ 6 = 13455)	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	No (remainder 2)	A number is divisible by 8 if the last three digits make a multiple of 8.
9	Yes (80730 ÷ 9 = 8970)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (80730 ÷ 10 = 8073)	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	No (remainder 6)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 80730 a prime number?

No. 80730 = 2 × $3^{3}$ × 5 × 13 × 23, so it is divisible by 2.

What are the factors of 80730?

1, 2, 3, 5, 6, 9, 10, 13, 15, 18, 23, 26, 27, 30, 39, 45, 46, 54, 65, 69, 78, 90, 115, 117, 130, 135, 138, 195, 207, 230, 234, 270, 299, 345, 351, 390, 414, 585, 598, 621, 690, 702, 897, 1035, 1170, 1242, 1495, 1755, 1794, 2070, 2691, 2990, 3105, 3510, 4485, 5382, 6210, 8073, 8970, 13455, 16146, 26910, 40365, 80730.

What is 80730 in binary?

10011101101011010 (hexadecimal 13B5A, octal 235532).

What is the square root of 80730?

About 284.1303, exactly 3√8970.

Is 80730 divisible by 3?

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

What is special about the number 80730?

80730 is a Harshad number: divisible by its digit sum 18.