The number 67500

Q: Is 67500 a prime number?

No. 67500 = 2^2 × 3^3 × 5^4, so it is divisible by 2.

67500 is a composite number with 60 divisors. Its prime factorisation is $2^{2}$ × $3^{3}$ × $5^{4}$ . Divisors (60): 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 27, 30, 36 … 67500.

Number

Pick any whole number from 1 to 100,000.

67500 = 2^{2} \times 3^{3} \times 5^{4}

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How to work it out

1
What is special about 67500: a Harshad number: divisible by its digit sum 18.
2
67500 is composite. Its prime factorisation is
$67500 = 2^{2} \times 3^{3} \times 5^{4}$
3
The divisors add up to 218680; without 67500 itself that is 151180, so 67500 is abundant (151180 is more than 67500). Euler's totient φ(67500) = 18000 numbers up to 67500 share no factor with it.
4
The digits of 67500 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 60 steps to reach 1.

LaTeX source of the formulas on this page

\[ 67500 = 2^{2} \times 3^{3} \times 5^{4} \]

67500 at a glance

Property	Value
Type	composite
Number of divisors	60
Sum of divisors	218680
Euler totient φ(n)	18000
Square	4556250000
Cube	307546875000000
Square root	259.807621 (= 150√3)
Digit sum / digital root	18 / 9
Collatz steps to 1	60
Scientific notation	6.75 × $10^{4}$

67500 in other forms

Form	Value
In words	sixty-seven thousand five hundred
Binary (base 2)	10000011110101100
Octal (base 8)	203654
Hexadecimal (base 16)	107AC
Base 3	10102121000
As time	67500 seconds = 18 h 45 min 0 s

Is 67500 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (67500 ÷ 2 = 33750)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (67500 ÷ 3 = 22500)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (67500 ÷ 4 = 16875)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (67500 ÷ 5 = 13500)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (67500 ÷ 6 = 11250)	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	Yes (67500 ÷ 9 = 7500)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (67500 ÷ 10 = 6750)	A number is divisible by 10 if the last digit is 0.
11	No (remainder 4)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (67500 ÷ 12 = 5625)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 67500 a prime number?

No. 67500 = $2^{2}$ × $3^{3}$ × $5^{4}$ , so it is divisible by 2.

What are the factors of 67500?

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 27, 30, 36, 45, 50, 54, 60, 75, 90, 100, 108, 125, 135, 150, 180, 225, 250, 270, 300, 375, 450, 500, 540, 625, 675, 750, 900, 1125, 1250, 1350, 1500, 1875, 2250, 2500, 2700, 3375, 3750, 4500, 5625, 6750, 7500, 11250, 13500, 16875, 22500, 33750, 67500.

What is 67500 in binary?

10000011110101100 (hexadecimal 107AC, octal 203654).

What is the square root of 67500?

About 259.8076, exactly 150√3.

Is 67500 divisible by 3?

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

What is special about the number 67500?

67500 is a Harshad number: divisible by its digit sum 18.