The number 54180

Q: Is 54180 a prime number?

No. 54180 = 2^2 × 3^2 × 5 × 7 × 43, so it is divisible by 2.

54180 is a composite number with 72 divisors. Its prime factorisation is $2^{2}$ × $3^{2}$ × 5 × 7 × 43. Divisors (72): 1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 28 … 54180.

Number

Pick any whole number from 1 to 100,000.

54180 = 2^{2} \times 3^{2} \times 5 \times 7 \times 43

Explain it step by step in chat Make a short video of it

How to work it out

1
What is special about 54180: a Harshad number: divisible by its digit sum 18.
2
54180 is composite. Its prime factorisation is
$54180 = 2^{2} \times 3^{2} \times 5 \times 7 \times 43$
3
The divisors add up to 192192; without 54180 itself that is 138012, so 54180 is abundant (138012 is more than 54180). Euler's totient φ(54180) = 12096 numbers up to 54180 share no factor with it.
4
The digits of 54180 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 184 steps to reach 1.

LaTeX source of the formulas on this page

\[ 54180 = 2^{2} \times 3^{2} \times 5 \times 7 \times 43 \]

54180 at a glance

Property	Value
Type	composite
Number of divisors	72
Sum of divisors	192192
Euler totient φ(n)	12096
Square	2935472400
Cube	159043894632000
Square root	232.765977 (= 6√1505)
Digit sum / digital root	18 / 9
Collatz steps to 1	184
Scientific notation	5.418 × $10^{4}$

54180 in other forms

Form	Value
In words	fifty-four thousand one hundred and eighty
Binary (base 2)	1101001110100100
Octal (base 8)	151644
Hexadecimal (base 16)	D3A4
Base 3	2202022200
As time	54180 seconds = 15 h 3 min 0 s

Is 54180 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (54180 ÷ 2 = 27090)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (54180 ÷ 3 = 18060)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (54180 ÷ 4 = 13545)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (54180 ÷ 5 = 10836)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (54180 ÷ 6 = 9030)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	Yes (54180 ÷ 7 = 7740)	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 (54180 ÷ 9 = 6020)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (54180 ÷ 10 = 5418)	A number is divisible by 10 if the last digit is 0.
11	No (remainder 5)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (54180 ÷ 12 = 4515)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 54180 a prime number?

No. 54180 = $2^{2}$ × $3^{2}$ × 5 × 7 × 43, so it is divisible by 2.

What are the factors of 54180?

1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 28, 30, 35, 36, 42, 43, 45, 60, 63, 70, 84, 86, 90, 105, 126, 129, 140, 172, 180, 210, 215, 252, 258, 301, 315, 387, 420, 430, 516, 602, 630, 645, 774, 860, 903, 1204, 1260, 1290, 1505, 1548, 1806, 1935, 2580, 2709, 3010, 3612, 3870, 4515, 5418, 6020, 7740, 9030, 10836, 13545, 18060, 27090, 54180.

What is 54180 in binary?

1101001110100100 (hexadecimal D3A4, octal 151644).

What is the square root of 54180?

About 232.7660, exactly 6√1505.

Is 54180 divisible by 3?

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

What is special about the number 54180?

54180 is a Harshad number: divisible by its digit sum 18.