The number 88500

Q: Is 88500 a prime number?

No. 88500 = 2^2 × 3 × 5^3 × 59, so it is divisible by 2.

88500 is a composite number with 48 divisors. Its prime factorisation is $2^{2}$ × 3 × $5^{3}$ × 59. Divisors (48): 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 59, 60, 75 … 88500.

Number

Pick any whole number from 1 to 100,000.

88500 = 2^{2} \times 3 \times 5^{3} \times 59

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How to work it out

1
88500 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
2
88500 is composite. Its prime factorisation is
$88500 = 2^{2} \times 3 \times 5^{3} \times 59$
3
The divisors add up to 262080; without 88500 itself that is 173580, so 88500 is abundant (173580 is more than 88500). Euler's totient φ(88500) = 23200 numbers up to 88500 share no factor with it.
4
The digits of 88500 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 45 steps to reach 1.

LaTeX source of the formulas on this page

\[ 88500 = 2^{2} \times 3 \times 5^{3} \times 59 \]

88500 at a glance

Property	Value
Type	composite
Number of divisors	48
Sum of divisors	262080
Euler totient φ(n)	23200
Square	7832250000
Cube	693154125000000
Square root	297.489496 (= 10√885)
Digit sum / digital root	21 / 3
Collatz steps to 1	45
Scientific notation	8.85 × $10^{4}$

88500 in other forms

Form	Value
In words	eighty-eight thousand five hundred
Binary (base 2)	10101100110110100
Octal (base 8)	254664
Hexadecimal (base 16)	159B4
Base 3	11111101210
As time	88500 seconds = 24 h 35 min 0 s

Is 88500 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (88500 ÷ 2 = 44250)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (88500 ÷ 3 = 29500)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (88500 ÷ 4 = 22125)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (88500 ÷ 5 = 17700)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (88500 ÷ 6 = 14750)	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 4)	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 (88500 ÷ 10 = 8850)	A number is divisible by 10 if the last digit is 0.
11	No (remainder 5)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (88500 ÷ 12 = 7375)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 88500 a prime number?

No. 88500 = $2^{2}$ × 3 × $5^{3}$ × 59, so it is divisible by 2.

What are the factors of 88500?

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 59, 60, 75, 100, 118, 125, 150, 177, 236, 250, 295, 300, 354, 375, 500, 590, 708, 750, 885, 1180, 1475, 1500, 1770, 2950, 3540, 4425, 5900, 7375, 8850, 14750, 17700, 22125, 29500, 44250, 88500.

What is 88500 in binary?

10101100110110100 (hexadecimal 159B4, octal 254664).

What is the square root of 88500?

About 297.4895, exactly 10√885.

Is 88500 divisible by 3?

Yes. Its digits add up to 21, a multiple of 3.

What is special about the number 88500?

It is a composite number with 48 divisors.