The number 40401

No. 40401 = 3^2 × 67^2, so it is divisible by 3.

40401 is a perfect square (201²). Its prime factorisation is $3^{2}$ × $67^{2}$ . Divisors (9): 1, 3, 9, 67, 201, 603, 4489, 13467, 40401.

Number

Pick any whole number from 1 to 100,000.

40401 = 3^{2} \times 67^{2}

How to work it out

1
What is special about 40401: a perfect square (201²); a Harshad number: divisible by its digit sum 9.
2
40401 is composite. Its prime factorisation is
$40401 = 3^{2} \times 67^{2}$
3
The divisors add up to 59241; without 40401 itself that is 18840, so 40401 is deficient (18840 is less than 40401). Euler's totient φ(40401) = 26532 numbers up to 40401 share no factor with it.
4
The digits of 40401 add up to 9, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 88 steps to reach 1.

LaTeX source of the formulas on this page

\[ 40401 = 3^{2} \times 67^{2} \]

Form	Value
In words	forty thousand four hundred and one
Binary (base 2)	1001110111010001
Octal (base 8)	116721
Hexadecimal (base 16)	9DD1
Base 3	2001102100
As time	40401 seconds = 11 h 13 min 21 s

Divisor	Answer	Rule
2	No (remainder 1)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (40401 ÷ 3 = 13467)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	No (remainder 1)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	No (remainder 1)	A number is divisible by 5 if the last digit is 0 or 5.
6	No (remainder 3)	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 1)	A number is divisible by 8 if the last three digits make a multiple of 8.
9	Yes (40401 ÷ 9 = 4489)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	No (remainder 1)	A number is divisible by 10 if the last digit is 0.
11	No (remainder 9)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	No (remainder 9)	A number is divisible by 12 if it is divisible by both 3 and 4.

Is 40401 a prime number?

No. 40401 = $3^{2}$ × $67^{2}$ , so it is divisible by 3.

What are the factors of 40401?

1, 3, 9, 67, 201, 603, 4489, 13467, 40401.

What is 40401 in binary?

1001110111010001 (hexadecimal 9DD1, octal 116721).

What is the square root of 40401?

201, because 201 × 201 = 40401.

Is 40401 divisible by 3?

Yes. Its digits add up to 9, a multiple of 3.

What is special about the number 40401?

40401 is a perfect square (201²); a Harshad number: divisible by its digit sum 9.