The number 76500

Q: Is 76500 a prime number?

No. 76500 = 2^2 × 3^2 × 5^3 × 17, so it is divisible by 2.

76500 is a composite number with 72 divisors. Its prime factorisation is $2^{2}$ × $3^{2}$ × $5^{3}$ × 17. Divisors (72): 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 17, 18, 20, 25, 30, 34 … 76500.

Number

Pick any whole number from 1 to 100,000.

76500 = 2^{2} \times 3^{2} \times 5^{3} \times 17

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How to work it out

1
What is special about 76500: a Harshad number: divisible by its digit sum 18.
2
76500 is composite. Its prime factorisation is
$76500 = 2^{2} \times 3^{2} \times 5^{3} \times 17$
3
The divisors add up to 255528; without 76500 itself that is 179028, so 76500 is abundant (179028 is more than 76500). Euler's totient φ(76500) = 19200 numbers up to 76500 share no factor with it.
4
The digits of 76500 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 125 steps to reach 1.

LaTeX source of the formulas on this page

\[ 76500 = 2^{2} \times 3^{2} \times 5^{3} \times 17 \]

76500 at a glance

Property	Value
Type	composite
Number of divisors	72
Sum of divisors	255528
Euler totient φ(n)	19200
Square	5852250000
Cube	447697125000000
Square root	276.586334 (= 30√85)
Digit sum / digital root	18 / 9
Collatz steps to 1	125
Scientific notation	7.65 × $10^{4}$

76500 in other forms

Form	Value
In words	seventy-six thousand five hundred
Binary (base 2)	10010101011010100
Octal (base 8)	225324
Hexadecimal (base 16)	12AD4
Base 3	10212221100
As time	76500 seconds = 21 h 15 min 0 s

Is 76500 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (76500 ÷ 2 = 38250)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (76500 ÷ 3 = 25500)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (76500 ÷ 4 = 19125)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (76500 ÷ 5 = 15300)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (76500 ÷ 6 = 12750)	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	No (remainder 4)	A number is divisible by 8 if the last three digits make a multiple of 8.
9	Yes (76500 ÷ 9 = 8500)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (76500 ÷ 10 = 7650)	A number is divisible by 10 if the last digit is 0.
11	No (remainder 6)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (76500 ÷ 12 = 6375)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 76500 a prime number?

No. 76500 = $2^{2}$ × $3^{2}$ × $5^{3}$ × 17, so it is divisible by 2.

What are the factors of 76500?

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 17, 18, 20, 25, 30, 34, 36, 45, 50, 51, 60, 68, 75, 85, 90, 100, 102, 125, 150, 153, 170, 180, 204, 225, 250, 255, 300, 306, 340, 375, 425, 450, 500, 510, 612, 750, 765, 850, 900, 1020, 1125, 1275, 1500, 1530, 1700, 2125, 2250, 2550, 3060, 3825, 4250, 4500, 5100, 6375, 7650, 8500, 12750, 15300, 19125, 25500, 38250, 76500.

What is 76500 in binary?

10010101011010100 (hexadecimal 12AD4, octal 225324).

What is the square root of 76500?

About 276.5863, exactly 30√85.

Is 76500 divisible by 3?

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

What is special about the number 76500?

76500 is a Harshad number: divisible by its digit sum 18.