The number 61800

Q: Is 61800 a prime number?

No. 61800 = 2^3 × 3 × 5^2 × 103, so it is divisible by 2.

61800 is a composite number with 48 divisors. Its prime factorisation is $2^{3}$ × 3 × $5^{2}$ × 103. Divisors (48): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50 … 61800.

Number

Pick any whole number from 1 to 100,000.

61800 = 2^{3} \times 3 \times 5^{2} \times 103

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How to work it out

1
What is special about 61800: a Harshad number: divisible by its digit sum 15.
2
61800 is composite. Its prime factorisation is
$61800 = 2^{3} \times 3 \times 5^{2} \times 103$
3
The divisors add up to 193440; without 61800 itself that is 131640, so 61800 is abundant (131640 is more than 61800). Euler's totient φ(61800) = 16320 numbers up to 61800 share no factor with it.
4
The digits of 61800 add up to 15, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 148 steps to reach 1.

LaTeX source of the formulas on this page

\[ 61800 = 2^{3} \times 3 \times 5^{2} \times 103 \]

61800 at a glance

Property	Value
Type	composite
Number of divisors	48
Sum of divisors	193440
Euler totient φ(n)	16320
Square	3819240000
Cube	236029032000000
Square root	248.596058 (= 10√618)
Digit sum / digital root	15 / 6
Collatz steps to 1	148
Scientific notation	6.18 × $10^{4}$

61800 in other forms

Form	Value
In words	sixty-one thousand eight hundred
Binary (base 2)	1111000101101000
Octal (base 8)	170550
Hexadecimal (base 16)	F168
Base 3	10010202220
As time	61800 seconds = 17 h 10 min 0 s

Is 61800 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (61800 ÷ 2 = 30900)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (61800 ÷ 3 = 20600)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (61800 ÷ 4 = 15450)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (61800 ÷ 5 = 12360)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (61800 ÷ 6 = 10300)	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	Yes (61800 ÷ 8 = 7725)	A number is divisible by 8 if the last three digits make a multiple of 8.
9	No (remainder 6)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (61800 ÷ 10 = 6180)	A number is divisible by 10 if the last digit is 0.
11	No (remainder 2)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (61800 ÷ 12 = 5150)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 61800 a prime number?

No. 61800 = $2^{3}$ × 3 × $5^{2}$ × 103, so it is divisible by 2.

What are the factors of 61800?

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 103, 120, 150, 200, 206, 300, 309, 412, 515, 600, 618, 824, 1030, 1236, 1545, 2060, 2472, 2575, 3090, 4120, 5150, 6180, 7725, 10300, 12360, 15450, 20600, 30900, 61800.

What is 61800 in binary?

1111000101101000 (hexadecimal F168, octal 170550).

What is the square root of 61800?

About 248.5961, exactly 10√618.

Is 61800 divisible by 3?

Yes. Its digits add up to 15, a multiple of 3.

What is special about the number 61800?

61800 is a Harshad number: divisible by its digit sum 15.