The number 83580

Q: Is 83580 a prime number?

No. 83580 = 2^2 × 3 × 5 × 7 × 199, so it is divisible by 2.

83580 is a composite number with 48 divisors. Its prime factorisation is $2^{2}$ × 3 × 5 × 7 × 199. Divisors (48): 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35 … 83580.

Number

Pick any whole number from 1 to 100,000.

83580 = 2^{2} \times 3 \times 5 \times 7 \times 199

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How to work it out

1
83580 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
2
83580 is composite. Its prime factorisation is
$83580 = 2^{2} \times 3 \times 5 \times 7 \times 199$
3
The divisors add up to 268800; without 83580 itself that is 185220, so 83580 is abundant (185220 is more than 83580). Euler's totient φ(83580) = 19008 numbers up to 83580 share no factor with it.
4
The digits of 83580 add up to 24, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 257 steps to reach 1.

LaTeX source of the formulas on this page

\[ 83580 = 2^{2} \times 3 \times 5 \times 7 \times 199 \]

83580 at a glance

Property	Value
Type	composite
Number of divisors	48
Sum of divisors	268800
Euler totient φ(n)	19008
Square	6985616400
Cube	583857818712000
Square root	289.102058 (= 2√20895)
Digit sum / digital root	24 / 6
Collatz steps to 1	257
Scientific notation	8.358 × $10^{4}$

83580 in other forms

Form	Value
In words	eighty-three thousand five hundred and eighty
Binary (base 2)	10100011001111100
Octal (base 8)	243174
Hexadecimal (base 16)	1467C
Base 3	11020122120
As time	83580 seconds = 23 h 13 min 0 s

Is 83580 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (83580 ÷ 2 = 41790)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (83580 ÷ 3 = 27860)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (83580 ÷ 4 = 20895)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (83580 ÷ 5 = 16716)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (83580 ÷ 6 = 13930)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	Yes (83580 ÷ 7 = 11940)	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 (83580 ÷ 10 = 8358)	A number is divisible by 10 if the last digit is 0.
11	No (remainder 2)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (83580 ÷ 12 = 6965)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 83580 a prime number?

No. 83580 = $2^{2}$ × 3 × 5 × 7 × 199, so it is divisible by 2.

What are the factors of 83580?

1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 199, 210, 398, 420, 597, 796, 995, 1194, 1393, 1990, 2388, 2786, 2985, 3980, 4179, 5572, 5970, 6965, 8358, 11940, 13930, 16716, 20895, 27860, 41790, 83580.

What is 83580 in binary?

10100011001111100 (hexadecimal 1467C, octal 243174).

What is the square root of 83580?

About 289.1021, exactly 2√20895.

Is 83580 divisible by 3?

Yes. Its digits add up to 24, a multiple of 3.

What is special about the number 83580?

It is a composite number with 48 divisors.