The number 38416

Q: Is 38416 a prime number?

No. 38416 = 2^4 × 7^4, so it is divisible by 2.

Q: What is special about the number 38416?

38416 is a perfect power (14^4); a perfect square (196²).

38416 is a perfect power ( $14^{4}$ ) and a perfect square (196²). Its prime factorisation is $2^{4}$ × $7^{4}$ . Divisors (25): 1, 2, 4, 7, 8, 14, 16, 28, 49, 56, 98, 112, 196, 343, 392, 686 … 38416.

Number

Pick any whole number from 1 to 100,000.

38416 = 2^{4} \times 7^{4}

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How to work it out

1
What is special about 38416: a perfect power ( $14^{4}$ ); a perfect square (196²).
2
38416 is composite. Its prime factorisation is
$38416 = 2^{4} \times 7^{4}$
3
The divisors add up to 86831; without 38416 itself that is 48415, so 38416 is abundant (48415 is more than 38416). Euler's totient φ(38416) = 16464 numbers up to 38416 share no factor with it.
4
The digits of 38416 add up to 22, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 168 steps to reach 1.

LaTeX source of the formulas on this page

\[ 38416 = 2^{4} \times 7^{4} \]

38416 at a glance

Property	Value
Type	composite
Number of divisors	25
Sum of divisors	86831
Euler totient φ(n)	16464
Square	1475789056
Cube	56693912375296
Square root	196
Digit sum / digital root	22 / 4
Collatz steps to 1	168
Scientific notation	3.8416 × $10^{4}$
Perfect power	$14^{4}$

38416 in other forms

Form	Value
In words	thirty-eight thousand four hundred and sixteen
Binary (base 2)	1001011000010000
Octal (base 8)	113020
Hexadecimal (base 16)	9610
Base 3	1221200211
As time	38416 seconds = 10 h 40 min 16 s

Is 38416 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (38416 ÷ 2 = 19208)	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 (38416 ÷ 4 = 9604)	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 4)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	Yes (38416 ÷ 7 = 5488)	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 (38416 ÷ 8 = 4802)	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 6)	A number is divisible by 10 if the last digit is 0.
11	No (remainder 4)	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.

Questions

Is 38416 a prime number?

No. 38416 = $2^{4}$ × $7^{4}$ , so it is divisible by 2.

What are the factors of 38416?

1, 2, 4, 7, 8, 14, 16, 28, 49, 56, 98, 112, 196, 343, 392, 686, 784, 1372, 2401, 2744, 4802, 5488, 9604, 19208, 38416.

What is 38416 in binary?

1001011000010000 (hexadecimal 9610, octal 113020).

What is the square root of 38416?

196, because 196 × 196 = 38416.

Is 38416 divisible by 3?

No. Its digits add up to 22, which is not a multiple of 3.

What is special about the number 38416?

38416 is a perfect power ( $14^{4}$ ); a perfect square (196²).