The number 83700

Q: Is 83700 a prime number?

No. 83700 = 2^2 × 3^3 × 5^2 × 31, so it is divisible by 2.

83700 is a composite number with 72 divisors. Its prime factorisation is $2^{2}$ × $3^{3}$ × $5^{2}$ × 31. Divisors (72): 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 27, 30, 31 … 83700.

Number

Pick any whole number from 1 to 100,000.

83700 = 2^{2} \times 3^{3} \times 5^{2} \times 31

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How to work it out

1
What is special about 83700: a Harshad number: divisible by its digit sum 18.
2
83700 is composite. Its prime factorisation is
$83700 = 2^{2} \times 3^{3} \times 5^{2} \times 31$
3
The divisors add up to 277760; without 83700 itself that is 194060, so 83700 is abundant (194060 is more than 83700). Euler's totient φ(83700) = 21600 numbers up to 83700 share no factor with it.
4
The digits of 83700 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 133 steps to reach 1.

LaTeX source of the formulas on this page

\[ 83700 = 2^{2} \times 3^{3} \times 5^{2} \times 31 \]

83700 at a glance

Property	Value
Type	composite
Number of divisors	72
Sum of divisors	277760
Euler totient φ(n)	21600
Square	7005690000
Cube	586376253000000
Square root	289.309523 (= 30√93)
Digit sum / digital root	18 / 9
Collatz steps to 1	133
Scientific notation	8.37 × $10^{4}$

83700 in other forms

Form	Value
In words	eighty-three thousand seven hundred
Binary (base 2)	10100011011110100
Octal (base 8)	243364
Hexadecimal (base 16)	146F4
Base 3	11020211000
As time	83700 seconds = 23 h 15 min 0 s

Is 83700 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (83700 ÷ 2 = 41850)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (83700 ÷ 3 = 27900)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (83700 ÷ 4 = 20925)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (83700 ÷ 5 = 16740)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (83700 ÷ 6 = 13950)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	No (remainder 1)	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 (83700 ÷ 9 = 9300)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (83700 ÷ 10 = 8370)	A number is divisible by 10 if the last digit is 0.
11	No (remainder 1)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (83700 ÷ 12 = 6975)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 83700 a prime number?

No. 83700 = $2^{2}$ × $3^{3}$ × $5^{2}$ × 31, so it is divisible by 2.

What are the factors of 83700?

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 27, 30, 31, 36, 45, 50, 54, 60, 62, 75, 90, 93, 100, 108, 124, 135, 150, 155, 180, 186, 225, 270, 279, 300, 310, 372, 450, 465, 540, 558, 620, 675, 775, 837, 900, 930, 1116, 1350, 1395, 1550, 1674, 1860, 2325, 2700, 2790, 3100, 3348, 4185, 4650, 5580, 6975, 8370, 9300, 13950, 16740, 20925, 27900, 41850, 83700.

What is 83700 in binary?

10100011011110100 (hexadecimal 146F4, octal 243364).

What is the square root of 83700?

About 289.3095, exactly 30√93.

Is 83700 divisible by 3?

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

What is special about the number 83700?

83700 is a Harshad number: divisible by its digit sum 18.