The number 85140

Q: Is 85140 a prime number?

No. 85140 = 2^2 × 3^2 × 5 × 11 × 43, so it is divisible by 2.

85140 is a composite number with 72 divisors. Its prime factorisation is $2^{2}$ × $3^{2}$ × 5 × 11 × 43. Divisors (72): 1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 15, 18, 20, 22, 30, 33 … 85140.

Number

Pick any whole number from 1 to 100,000.

85140 = 2^{2} \times 3^{2} \times 5 \times 11 \times 43

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How to work it out

1
What is special about 85140: a Harshad number: divisible by its digit sum 18.
2
85140 is composite. Its prime factorisation is
$85140 = 2^{2} \times 3^{2} \times 5 \times 11 \times 43$
3
The divisors add up to 288288; without 85140 itself that is 203148, so 85140 is abundant (203148 is more than 85140). Euler's totient φ(85140) = 20160 numbers up to 85140 share no factor with it.
4
The digits of 85140 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 58 steps to reach 1.

LaTeX source of the formulas on this page

\[ 85140 = 2^{2} \times 3^{2} \times 5 \times 11 \times 43 \]

85140 at a glance

Property	Value
Type	composite
Number of divisors	72
Sum of divisors	288288
Euler totient φ(n)	20160
Square	7248819600
Cube	617164500744000
Square root	291.787594 (= 6√2365)
Digit sum / digital root	18 / 9
Collatz steps to 1	58
Scientific notation	8.514 × $10^{4}$

85140 in other forms

Form	Value
In words	eighty-five thousand one hundred and forty
Binary (base 2)	10100110010010100
Octal (base 8)	246224
Hexadecimal (base 16)	14C94
Base 3	11022210100
As time	85140 seconds = 23 h 39 min 0 s

Is 85140 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (85140 ÷ 2 = 42570)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (85140 ÷ 3 = 28380)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (85140 ÷ 4 = 21285)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (85140 ÷ 5 = 17028)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (85140 ÷ 6 = 14190)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	No (remainder 6)	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 (85140 ÷ 9 = 9460)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (85140 ÷ 10 = 8514)	A number is divisible by 10 if the last digit is 0.
11	Yes (85140 ÷ 11 = 7740)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (85140 ÷ 12 = 7095)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 85140 a prime number?

No. 85140 = $2^{2}$ × $3^{2}$ × 5 × 11 × 43, so it is divisible by 2.

What are the factors of 85140?

1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 15, 18, 20, 22, 30, 33, 36, 43, 44, 45, 55, 60, 66, 86, 90, 99, 110, 129, 132, 165, 172, 180, 198, 215, 220, 258, 330, 387, 396, 430, 473, 495, 516, 645, 660, 774, 860, 946, 990, 1290, 1419, 1548, 1892, 1935, 1980, 2365, 2580, 2838, 3870, 4257, 4730, 5676, 7095, 7740, 8514, 9460, 14190, 17028, 21285, 28380, 42570, 85140.

What is 85140 in binary?

10100110010010100 (hexadecimal 14C94, octal 246224).

What is the square root of 85140?

About 291.7876, exactly 6√2365.

Is 85140 divisible by 3?

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

What is special about the number 85140?

85140 is a Harshad number: divisible by its digit sum 18.