The number 20164

No. 20164 = 2^2 × 71^2, so it is divisible by 2.

20164 is a perfect square (142²). Its prime factorisation is $2^{2}$ × $71^{2}$ . Divisors (9): 1, 2, 4, 71, 142, 284, 5041, 10082, 20164.

Number

Pick any whole number from 1 to 100,000.

20164 = 2^{2} \times 71^{2}

How to work it out

1
What is special about 20164: a perfect square (142²).
2
20164 is composite. Its prime factorisation is
$20164 = 2^{2} \times 71^{2}$
3
The divisors add up to 35791; without 20164 itself that is 15627, so 20164 is deficient (15627 is less than 20164). Euler's totient φ(20164) = 9940 numbers up to 20164 share no factor with it.
4
The digits of 20164 add up to 13, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 43 steps to reach 1.

LaTeX source of the formulas on this page

\[ 20164 = 2^{2} \times 71^{2} \]

Form	Value
In words	twenty thousand one hundred and sixty-four
Binary (base 2)	100111011000100
Octal (base 8)	47304
Hexadecimal (base 16)	4EC4
Base 3	1000122211
As time	20164 seconds = 5 h 36 min 4 s

Divisor	Answer	Rule
2	Yes (20164 ÷ 2 = 10082)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	No (remainder 1)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (20164 ÷ 4 = 5041)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	No (remainder 4)	A number is divisible by 5 if the last digit is 0 or 5.
6	No (remainder 4)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	No (remainder 4)	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 4)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	No (remainder 4)	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	No (remainder 4)	A number is divisible by 12 if it is divisible by both 3 and 4.

Is 20164 a prime number?

No. 20164 = $2^{2}$ × $71^{2}$ , so it is divisible by 2.

What are the factors of 20164?

1, 2, 4, 71, 142, 284, 5041, 10082, 20164.

What is 20164 in binary?

100111011000100 (hexadecimal 4EC4, octal 47304).

What is the square root of 20164?

142, because 142 × 142 = 20164.

Is 20164 divisible by 3?

No. Its digits add up to 13, which is not a multiple of 3.

What is special about the number 20164?

20164 is a perfect square (142²).