The number 97500

Q: Is 97500 a prime number?

No. 97500 = 2^2 × 3 × 5^4 × 13, so it is divisible by 2.

97500 is a composite number with 60 divisors. Its prime factorisation is $2^{2}$ × 3 × $5^{4}$ × 13. Divisors (60): 1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 20, 25, 26, 30, 39, 50 … 97500.

Number

Pick any whole number from 1 to 100,000.

97500 = 2^{2} \times 3 \times 5^{4} \times 13

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How to work it out

1
97500 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
2
97500 is composite. Its prime factorisation is
$97500 = 2^{2} \times 3 \times 5^{4} \times 13$
3
The divisors add up to 306152; without 97500 itself that is 208652, so 97500 is abundant (208652 is more than 97500). Euler's totient φ(97500) = 24000 numbers up to 97500 share no factor with it.
4
The digits of 97500 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 97 steps to reach 1.

LaTeX source of the formulas on this page

\[ 97500 = 2^{2} \times 3 \times 5^{4} \times 13 \]

97500 at a glance

Property	Value
Type	composite
Number of divisors	60
Sum of divisors	306152
Euler totient φ(n)	24000
Square	9506250000
Cube	926859375000000
Square root	312.249900 (= 50√39)
Digit sum / digital root	21 / 3
Collatz steps to 1	97
Scientific notation	9.75 × $10^{4}$

97500 in other forms

Form	Value
In words	ninety-seven thousand five hundred
Binary (base 2)	10111110011011100
Octal (base 8)	276334
Hexadecimal (base 16)	17CDC
Base 3	11221202010
As time	97500 seconds = 27 h 5 min 0 s

Is 97500 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (97500 ÷ 2 = 48750)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (97500 ÷ 3 = 32500)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (97500 ÷ 4 = 24375)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (97500 ÷ 5 = 19500)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (97500 ÷ 6 = 16250)	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	No (remainder 3)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (97500 ÷ 10 = 9750)	A number is divisible by 10 if the last digit is 0.
11	No (remainder 7)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (97500 ÷ 12 = 8125)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 97500 a prime number?

No. 97500 = $2^{2}$ × 3 × $5^{4}$ × 13, so it is divisible by 2.

What are the factors of 97500?

1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 20, 25, 26, 30, 39, 50, 52, 60, 65, 75, 78, 100, 125, 130, 150, 156, 195, 250, 260, 300, 325, 375, 390, 500, 625, 650, 750, 780, 975, 1250, 1300, 1500, 1625, 1875, 1950, 2500, 3250, 3750, 3900, 4875, 6500, 7500, 8125, 9750, 16250, 19500, 24375, 32500, 48750, 97500.

What is 97500 in binary?

10111110011011100 (hexadecimal 17CDC, octal 276334).

What is the square root of 97500?

About 312.2499, exactly 50√39.

Is 97500 divisible by 3?

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

What is special about the number 97500?

It is a composite number with 60 divisors.