The number 88140

Q: Is 88140 a prime number?

No. 88140 = 2^2 × 3 × 5 × 13 × 113, so it is divisible by 2.

88140 is a composite number with 48 divisors. Its prime factorisation is $2^{2}$ × 3 × 5 × 13 × 113. Divisors (48): 1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 20, 26, 30, 39, 52, 60 … 88140.

Number

Pick any whole number from 1 to 100,000.

88140 = 2^{2} \times 3 \times 5 \times 13 \times 113

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How to work it out

1
88140 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
2
88140 is composite. Its prime factorisation is
$88140 = 2^{2} \times 3 \times 5 \times 13 \times 113$
3
The divisors add up to 268128; without 88140 itself that is 179988, so 88140 is abundant (179988 is more than 88140). Euler's totient φ(88140) = 21504 numbers up to 88140 share no factor with it.
4
The digits of 88140 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 164 steps to reach 1.

LaTeX source of the formulas on this page

\[ 88140 = 2^{2} \times 3 \times 5 \times 13 \times 113 \]

88140 at a glance

Property	Value
Type	composite
Number of divisors	48
Sum of divisors	268128
Euler totient φ(n)	21504
Square	7768659600
Cube	684729657144000
Square root	296.883816 (= 2√22035)
Digit sum / digital root	21 / 3
Collatz steps to 1	164
Scientific notation	8.814 × $10^{4}$

88140 in other forms

Form	Value
In words	eighty-eight thousand one hundred and forty
Binary (base 2)	10101100001001100
Octal (base 8)	254114
Hexadecimal (base 16)	1584C
Base 3	11110220110
As time	88140 seconds = 24 h 29 min 0 s

Is 88140 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (88140 ÷ 2 = 44070)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (88140 ÷ 3 = 29380)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (88140 ÷ 4 = 22035)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (88140 ÷ 5 = 17628)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (88140 ÷ 6 = 14690)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	No (remainder 3)	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 3)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (88140 ÷ 10 = 8814)	A number is divisible by 10 if the last digit is 0.
11	No (remainder 8)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (88140 ÷ 12 = 7345)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 88140 a prime number?

No. 88140 = $2^{2}$ × 3 × 5 × 13 × 113, so it is divisible by 2.

What are the factors of 88140?

1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 20, 26, 30, 39, 52, 60, 65, 78, 113, 130, 156, 195, 226, 260, 339, 390, 452, 565, 678, 780, 1130, 1356, 1469, 1695, 2260, 2938, 3390, 4407, 5876, 6780, 7345, 8814, 14690, 17628, 22035, 29380, 44070, 88140.

What is 88140 in binary?

10101100001001100 (hexadecimal 1584C, octal 254114).

What is the square root of 88140?

About 296.8838, exactly 2√22035.

Is 88140 divisible by 3?

Yes. Its digits add up to 21, a multiple of 3.

What is special about the number 88140?

It is a composite number with 48 divisors.