The number 61380

Q: Is 61380 a prime number?

No. 61380 = 2^2 × 3^2 × 5 × 11 × 31, so it is divisible by 2.

61380 is a composite number with 72 divisors. Its prime factorisation is $2^{2}$ × $3^{2}$ × 5 × 11 × 31. Divisors (72): 1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 15, 18, 20, 22, 30, 31 … 61380.

Number

Pick any whole number from 1 to 100,000.

61380 = 2^{2} \times 3^{2} \times 5 \times 11 \times 31

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How to work it out

1
What is special about 61380: a Harshad number: divisible by its digit sum 18.
2
61380 is composite. Its prime factorisation is
$61380 = 2^{2} \times 3^{2} \times 5 \times 11 \times 31$
3
The divisors add up to 209664; without 61380 itself that is 148284, so 61380 is abundant (148284 is more than 61380). Euler's totient φ(61380) = 14400 numbers up to 61380 share no factor with it.
4
The digits of 61380 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

\[ 61380 = 2^{2} \times 3^{2} \times 5 \times 11 \times 31 \]

61380 at a glance

Property	Value
Type	composite
Number of divisors	72
Sum of divisors	209664
Euler totient φ(n)	14400
Square	3767504400
Cube	231249420072000
Square root	247.749874 (= 6√1705)
Digit sum / digital root	18 / 9
Collatz steps to 1	60
Scientific notation	6.138 × $10^{4}$

61380 in other forms

Form	Value
In words	sixty-one thousand three hundred and eighty
Binary (base 2)	1110111111000100
Octal (base 8)	167704
Hexadecimal (base 16)	EFC4
Base 3	10010012100
As time	61380 seconds = 17 h 3 min 0 s

Is 61380 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (61380 ÷ 2 = 30690)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (61380 ÷ 3 = 20460)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (61380 ÷ 4 = 15345)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (61380 ÷ 5 = 12276)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (61380 ÷ 6 = 10230)	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	No (remainder 4)	A number is divisible by 8 if the last three digits make a multiple of 8.
9	Yes (61380 ÷ 9 = 6820)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (61380 ÷ 10 = 6138)	A number is divisible by 10 if the last digit is 0.
11	Yes (61380 ÷ 11 = 5580)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (61380 ÷ 12 = 5115)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 61380 a prime number?

No. 61380 = $2^{2}$ × $3^{2}$ × 5 × 11 × 31, so it is divisible by 2.

What are the factors of 61380?

1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 15, 18, 20, 22, 30, 31, 33, 36, 44, 45, 55, 60, 62, 66, 90, 93, 99, 110, 124, 132, 155, 165, 180, 186, 198, 220, 279, 310, 330, 341, 372, 396, 465, 495, 558, 620, 660, 682, 930, 990, 1023, 1116, 1364, 1395, 1705, 1860, 1980, 2046, 2790, 3069, 3410, 4092, 5115, 5580, 6138, 6820, 10230, 12276, 15345, 20460, 30690, 61380.

What is 61380 in binary?

1110111111000100 (hexadecimal EFC4, octal 167704).

What is the square root of 61380?

About 247.7499, exactly 6√1705.

Is 61380 divisible by 3?

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

What is special about the number 61380?

61380 is a Harshad number: divisible by its digit sum 18.