The number 60180

Q: Is 60180 a prime number?

No. 60180 = 2^2 × 3 × 5 × 17 × 59, so it is divisible by 2.

60180 is a composite number with 48 divisors. Its prime factorisation is $2^{2}$ × 3 × 5 × 17 × 59. Divisors (48): 1, 2, 3, 4, 5, 6, 10, 12, 15, 17, 20, 30, 34, 51, 59, 60 … 60180.

Number

Pick any whole number from 1 to 100,000.

60180 = 2^{2} \times 3 \times 5 \times 17 \times 59

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How to work it out

1
What is special about 60180: a Harshad number: divisible by its digit sum 15.
2
60180 is composite. Its prime factorisation is
$60180 = 2^{2} \times 3 \times 5 \times 17 \times 59$
3
The divisors add up to 181440; without 60180 itself that is 121260, so 60180 is abundant (121260 is more than 60180). Euler's totient φ(60180) = 14848 numbers up to 60180 share no factor with it.
4
The digits of 60180 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 42 steps to reach 1.

LaTeX source of the formulas on this page

\[ 60180 = 2^{2} \times 3 \times 5 \times 17 \times 59 \]

60180 at a glance

Property	Value
Type	composite
Number of divisors	48
Sum of divisors	181440
Euler totient φ(n)	14848
Square	3621632400
Cube	217949837832000
Square root	245.316123 (= 2√15045)
Digit sum / digital root	15 / 6
Collatz steps to 1	42
Scientific notation	6.018 × $10^{4}$

60180 in other forms

Form	Value
In words	sixty thousand one hundred and eighty
Binary (base 2)	1110101100010100
Octal (base 8)	165424
Hexadecimal (base 16)	EB14
Base 3	10001112220
As time	60180 seconds = 16 h 43 min 0 s

Is 60180 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (60180 ÷ 2 = 30090)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (60180 ÷ 3 = 20060)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (60180 ÷ 4 = 15045)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (60180 ÷ 5 = 12036)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (60180 ÷ 6 = 10030)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	No (remainder 1)	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 6)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (60180 ÷ 10 = 6018)	A number is divisible by 10 if the last digit is 0.
11	No (remainder 10)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (60180 ÷ 12 = 5015)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 60180 a prime number?

No. 60180 = $2^{2}$ × 3 × 5 × 17 × 59, so it is divisible by 2.

What are the factors of 60180?

1, 2, 3, 4, 5, 6, 10, 12, 15, 17, 20, 30, 34, 51, 59, 60, 68, 85, 102, 118, 170, 177, 204, 236, 255, 295, 340, 354, 510, 590, 708, 885, 1003, 1020, 1180, 1770, 2006, 3009, 3540, 4012, 5015, 6018, 10030, 12036, 15045, 20060, 30090, 60180.

What is 60180 in binary?

1110101100010100 (hexadecimal EB14, octal 165424).

What is the square root of 60180?

About 245.3161, exactly 2√15045.

Is 60180 divisible by 3?

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

What is special about the number 60180?

60180 is a Harshad number: divisible by its digit sum 15.