The number 83720

Q: Is 83720 a prime number?

No. 83720 = 2^3 × 5 × 7 × 13 × 23, so it is divisible by 2.

83720 is a composite number with 64 divisors. Its prime factorisation is $2^{3}$ × 5 × 7 × 13 × 23. Divisors (64): 1, 2, 4, 5, 7, 8, 10, 13, 14, 20, 23, 26, 28, 35, 40, 46 … 83720.

Number

Pick any whole number from 1 to 100,000.

83720 = 2^{3} \times 5 \times 7 \times 13 \times 23

Explain it step by step in chat Make a short video of it

How to work it out

1
What is special about 83720: a Harshad number: divisible by its digit sum 20.
2
83720 is composite. Its prime factorisation is
$83720 = 2^{3} \times 5 \times 7 \times 13 \times 23$
3
The divisors add up to 241920; without 83720 itself that is 158200, so 83720 is abundant (158200 is more than 83720). Euler's totient φ(83720) = 25344 numbers up to 83720 share no factor with it.
4
The digits of 83720 add up to 20, and repeating that until one digit is left gives the digital root 2. The Collatz sequence (halve if even, else 3n+1) takes 133 steps to reach 1.

LaTeX source of the formulas on this page

\[ 83720 = 2^{3} \times 5 \times 7 \times 13 \times 23 \]

83720 at a glance

Property	Value
Type	composite
Number of divisors	64
Sum of divisors	241920
Euler totient φ(n)	25344
Square	7009038400
Cube	586796694848000
Square root	289.344086 (= 2√20930)
Digit sum / digital root	20 / 2
Collatz steps to 1	133
Scientific notation	8.372 × $10^{4}$

83720 in other forms

Form	Value
In words	eighty-three thousand seven hundred and twenty
Binary (base 2)	10100011100001000
Octal (base 8)	243410
Hexadecimal (base 16)	14708
Base 3	11020211202
As time	83720 seconds = 23 h 15 min 20 s

Is 83720 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (83720 ÷ 2 = 41860)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	No (remainder 2)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (83720 ÷ 4 = 20930)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (83720 ÷ 5 = 16744)	A number is divisible by 5 if the last digit is 0 or 5.
6	No (remainder 2)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	Yes (83720 ÷ 7 = 11960)	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	Yes (83720 ÷ 8 = 10465)	A number is divisible by 8 if the last three digits make a multiple of 8.
9	No (remainder 2)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (83720 ÷ 10 = 8372)	A number is divisible by 10 if the last digit is 0.
11	No (remainder 10)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	No (remainder 8)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 83720 a prime number?

No. 83720 = $2^{3}$ × 5 × 7 × 13 × 23, so it is divisible by 2.

What are the factors of 83720?

1, 2, 4, 5, 7, 8, 10, 13, 14, 20, 23, 26, 28, 35, 40, 46, 52, 56, 65, 70, 91, 92, 104, 115, 130, 140, 161, 182, 184, 230, 260, 280, 299, 322, 364, 455, 460, 520, 598, 644, 728, 805, 910, 920, 1196, 1288, 1495, 1610, 1820, 2093, 2392, 2990, 3220, 3640, 4186, 5980, 6440, 8372, 10465, 11960, 16744, 20930, 41860, 83720.

What is 83720 in binary?

10100011100001000 (hexadecimal 14708, octal 243410).

What is the square root of 83720?

About 289.3441, exactly 2√20930.

Is 83720 divisible by 3?

No. Its digits add up to 20, which is not a multiple of 3.

What is special about the number 83720?

83720 is a Harshad number: divisible by its digit sum 20.