The number 73500

Q: Is 73500 a prime number?

No. 73500 = 2^2 × 3 × 5^3 × 7^2, so it is divisible by 2.

73500 is a composite number with 72 divisors. Its prime factorisation is $2^{2}$ × 3 × $5^{3}$ × $7^{2}$ . Divisors (72): 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 25, 28, 30 … 73500.

Number

Pick any whole number from 1 to 100,000.

73500 = 2^{2} \times 3 \times 5^{3} \times 7^{2}

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How to work it out

1
What is special about 73500: a Harshad number: divisible by its digit sum 15.
2
73500 is composite. Its prime factorisation is
$73500 = 2^{2} \times 3 \times 5^{3} \times 7^{2}$
3
The divisors add up to 248976; without 73500 itself that is 175476, so 73500 is abundant (175476 is more than 73500). Euler's totient φ(73500) = 16800 numbers up to 73500 share no factor with it.
4
The digits of 73500 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 63 steps to reach 1.

LaTeX source of the formulas on this page

\[ 73500 = 2^{2} \times 3 \times 5^{3} \times 7^{2} \]

73500 at a glance

Property	Value
Type	composite
Number of divisors	72
Sum of divisors	248976
Euler totient φ(n)	16800
Square	5402250000
Cube	397065375000000
Square root	271.108834 (= 70√15)
Digit sum / digital root	15 / 6
Collatz steps to 1	63
Scientific notation	7.35 × $10^{4}$

73500 in other forms

Form	Value
In words	seventy-three thousand five hundred
Binary (base 2)	10001111100011100
Octal (base 8)	217434
Hexadecimal (base 16)	11F1C
Base 3	10201211020
As time	73500 seconds = 20 h 25 min 0 s

Is 73500 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (73500 ÷ 2 = 36750)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (73500 ÷ 3 = 24500)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (73500 ÷ 4 = 18375)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (73500 ÷ 5 = 14700)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (73500 ÷ 6 = 12250)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	Yes (73500 ÷ 7 = 10500)	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 (73500 ÷ 10 = 7350)	A number is divisible by 10 if the last digit is 0.
11	No (remainder 9)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (73500 ÷ 12 = 6125)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 73500 a prime number?

No. 73500 = $2^{2}$ × 3 × $5^{3}$ × $7^{2}$ , so it is divisible by 2.

What are the factors of 73500?

1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 25, 28, 30, 35, 42, 49, 50, 60, 70, 75, 84, 98, 100, 105, 125, 140, 147, 150, 175, 196, 210, 245, 250, 294, 300, 350, 375, 420, 490, 500, 525, 588, 700, 735, 750, 875, 980, 1050, 1225, 1470, 1500, 1750, 2100, 2450, 2625, 2940, 3500, 3675, 4900, 5250, 6125, 7350, 10500, 12250, 14700, 18375, 24500, 36750, 73500.

What is 73500 in binary?

10001111100011100 (hexadecimal 11F1C, octal 217434).

What is the square root of 73500?

About 271.1088, exactly 70√15.

Is 73500 divisible by 3?

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

What is special about the number 73500?

73500 is a Harshad number: divisible by its digit sum 15.