The number 67800

Q: Is 67800 a prime number?

No. 67800 = 2^3 × 3 × 5^2 × 113, so it is divisible by 2.

67800 is a composite number with 48 divisors. Its prime factorisation is $2^{3}$ × 3 × $5^{2}$ × 113. Divisors (48): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50 … 67800.

Number

Pick any whole number from 1 to 100,000.

67800 = 2^{3} \times 3 \times 5^{2} \times 113

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How to work it out

1
67800 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
2
67800 is composite. Its prime factorisation is
$67800 = 2^{3} \times 3 \times 5^{2} \times 113$
3
The divisors add up to 212040; without 67800 itself that is 144240, so 67800 is abundant (144240 is more than 67800). Euler's totient φ(67800) = 17920 numbers up to 67800 share no factor with it.
4
The digits of 67800 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 112 steps to reach 1.

LaTeX source of the formulas on this page

\[ 67800 = 2^{3} \times 3 \times 5^{2} \times 113 \]

67800 at a glance

Property	Value
Type	composite
Number of divisors	48
Sum of divisors	212040
Euler totient φ(n)	17920
Square	4596840000
Cube	311665752000000
Square root	260.384331 (= 10√678)
Digit sum / digital root	21 / 3
Collatz steps to 1	112
Scientific notation	6.78 × $10^{4}$

67800 in other forms

Form	Value
In words	sixty-seven thousand eight hundred
Binary (base 2)	10000100011011000
Octal (base 8)	204330
Hexadecimal (base 16)	108D8
Base 3	10110000010
As time	67800 seconds = 18 h 50 min 0 s

Is 67800 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (67800 ÷ 2 = 33900)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (67800 ÷ 3 = 22600)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (67800 ÷ 4 = 16950)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (67800 ÷ 5 = 13560)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (67800 ÷ 6 = 11300)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	No (remainder 5)	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	Yes (67800 ÷ 8 = 8475)	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 (67800 ÷ 10 = 6780)	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 (67800 ÷ 12 = 5650)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 67800 a prime number?

No. 67800 = $2^{3}$ × 3 × $5^{2}$ × 113, so it is divisible by 2.

What are the factors of 67800?

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 113, 120, 150, 200, 226, 300, 339, 452, 565, 600, 678, 904, 1130, 1356, 1695, 2260, 2712, 2825, 3390, 4520, 5650, 6780, 8475, 11300, 13560, 16950, 22600, 33900, 67800.

What is 67800 in binary?

10000100011011000 (hexadecimal 108D8, octal 204330).

What is the square root of 67800?

About 260.3843, exactly 10√678.

Is 67800 divisible by 3?

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

What is special about the number 67800?

It is a composite number with 48 divisors.