The number 84100

Q: Is 84100 a prime number?

No. 84100 = 2^2 × 5^2 × 29^2, so it is divisible by 2.

84100 is a perfect square (290²). Its prime factorisation is $2^{2}$ × $5^{2}$ × $29^{2}$ . Divisors (27): 1, 2, 4, 5, 10, 20, 25, 29, 50, 58, 100, 116, 145, 290, 580, 725 … 84100.

Number

Pick any whole number from 1 to 100,000.

84100 = 2^{2} \times 5^{2} \times 29^{2}

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How to work it out

1
What is special about 84100: a perfect square (290²).
2
84100 is composite. Its prime factorisation is
$84100 = 2^{2} \times 5^{2} \times 29^{2}$
3
The divisors add up to 189007; without 84100 itself that is 104907, so 84100 is abundant (104907 is more than 84100). Euler's totient φ(84100) = 32480 numbers up to 84100 share no factor with it.
4
The digits of 84100 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 89 steps to reach 1.

LaTeX source of the formulas on this page

\[ 84100 = 2^{2} \times 5^{2} \times 29^{2} \]

84100 at a glance

Property	Value
Type	composite
Number of divisors	27
Sum of divisors	189007
Euler totient φ(n)	32480
Square	7072810000
Cube	594823321000000
Square root	290
Digit sum / digital root	13 / 4
Collatz steps to 1	89
Scientific notation	8.41 × $10^{4}$
Perfect power	$290^{2}$

84100 in other forms

Form	Value
In words	eighty-four thousand one hundred
Binary (base 2)	10100100010000100
Octal (base 8)	244204
Hexadecimal (base 16)	14884
Base 3	11021100211
As time	84100 seconds = 23 h 21 min 40 s

Is 84100 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (84100 ÷ 2 = 42050)	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 (84100 ÷ 4 = 21025)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (84100 ÷ 5 = 16820)	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 2)	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	Yes (84100 ÷ 10 = 8410)	A number is divisible by 10 if the last digit is 0.
11	No (remainder 5)	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 84100 a prime number?

No. 84100 = $2^{2}$ × $5^{2}$ × $29^{2}$ , so it is divisible by 2.

What are the factors of 84100?

1, 2, 4, 5, 10, 20, 25, 29, 50, 58, 100, 116, 145, 290, 580, 725, 841, 1450, 1682, 2900, 3364, 4205, 8410, 16820, 21025, 42050, 84100.

What is 84100 in binary?

10100100010000100 (hexadecimal 14884, octal 244204).

What is the square root of 84100?

290, because 290 × 290 = 84100.

Is 84100 divisible by 3?

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

What is special about the number 84100?

84100 is a perfect square (290²).